What is the equation of the line that passes, №18011144, 26.03.2023 05:48

Mathematics

What is the equation of the line that passes through the point (3, 5) and has a slope of -1/3

Step-by-step answer

P Answered by Specialist

$Y=-\frac{1}{3} + 6$

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Mathematics

What is the equation of the line that passes through the point (3, 5) and has a slope of -1/3

Step-by-step answer

P Answered by Master

Linear Equations

Linear equations are typically organized in slope-intercept form:

y=mx+b

m = slopeb = y-intercept (the value of y when the line crosses the y-axis)

To determine the equation of a line:

Find the slopePlug the slope into y=mx+bPlug in a point that falls on the line as (x,y)Solve for b

Solving the Question

We're given:

$m=-\dfrac{1}{3}$ The lines passes through the point (3,5)

y=mx+b

⇒ Plug the slope into the equation:

$y=-\dfrac{1}{3}x+b$

⇒ Plug in the given point (3,5) and determine the y-intercept:

$5=-\dfrac{1}{3}(3)+b\\\\5=-1+b\\\\b=6$

⇒ Plug this back into the equation along with the slope:

$y=-\dfrac{1}{3}x+6$

Answer

$y=-\dfrac{1}{3}x+6$

Mathematics

Which is the slope of the line that passes through the points (3,5) and (8,7)? 1. -1/2 2. 5/2 3. 2/5 4. 3/4

Step-by-step answer

P Answered by Master

17

Y = mx + b

m = (y2 - y1)/(x2 - x1) = (7-5)/(8-3) = 2/5

3. 2/5 is the slope of the line

Mathematics

Which is the slope of the line that passes through the points (3,5) and (8,7)? 1. -1/2 2. 5/2 3. 2/5 4. 3/4

Step-by-step answer

P Answered by Specialist

17

Y = mx + b

m = (y2 - y1)/(x2 - x1) = (7-5)/(8-3) = 2/5

3. 2/5 is the slope of the line

Mathematics

15 points can someone check my answers? 1. for the data in the table, does y vary directly with x? if it does write an equation for the direct variation.(x,y) (8,11) (16,22) (24,33) yes y=2.75x yes y=0.6875x*** yes y=1.375x no y does not vary directly with x ** (for #1, i m debating between b and d) 2.for the data in the table, does y vary directly with x? if it does write an equation for the direct variation. (x,y) (16,4) (32,16) (48,36) yes y=2x yes y=4x yes y=8x no y does not very directly with x*** 3. (time/hour,distance/miles)(4,233) (6,348)

Step-by-step answer

P Answered by PhD

1

2 and 9 are correct. The remainder need to be reconsidered.

Step-by-step explanation:

Your answer to 9 is correct, which means you have the appropriate signs for the point coordinates. In your other point-slope questions, one or more of the signs is incorrect. Use your good work as an example of how to choose the correct answers elsewhere.

1) When you have y = kx, you can find the value of k from ...

... k = y/x

When the variation is direct, this works for any (x, y) pair.

3) A unit rate is called a unit rate because it has 1 (a unit) in the denominator.

4a, 4b, ... all slope calculations. You managed to get it right in problem 9. Watch your signs.

10, 11 ... It can work well to put the x term on the same side with the y-term, then multiply the equation by the denominator value.

... (2/3)x + y = 7 . . . . add (2/3)x to both sides of the equation

... 2x + 3y = 21 . . . . . multiply by 3. (Standard form always has the leading coefficient positive.)

Whenever you consider making a term disappear from one side of the equation, think in terms of adding its opposite to both sides of the equation. This will give the result you want and is consistent with the properties of equality: whatever you do to one side of the equation you must also do to the other side of the equation. Other wording may have been used by your teacher or friends. This is the one true statement about transforming equations.

Mathematics

15 points can someone check my answers? 1. for the data in the table, does y vary directly with x? if it does write an equation for the direct variation.(x,y) (8,11) (16,22) (24,33) yes y=2.75x yes y=0.6875x*** yes y=1.375x no y does not vary directly with x ** (for #1, i m debating between b and d) 2.for the data in the table, does y vary directly with x? if it does write an equation for the direct variation. (x,y) (16,4) (32,16) (48,36) yes y=2x yes y=4x yes y=8x no y does not very directly with x*** 3. (time/hour,distance/miles)(4,233) (6,348)

Step-by-step answer

P Answered by PhD

1

2 and 9 are correct. The remainder need to be reconsidered.

Step-by-step explanation:

Your answer to 9 is correct, which means you have the appropriate signs for the point coordinates. In your other point-slope questions, one or more of the signs is incorrect. Use your good work as an example of how to choose the correct answers elsewhere.

1) When you have y = kx, you can find the value of k from ...

... k = y/x

When the variation is direct, this works for any (x, y) pair.

3) A unit rate is called a unit rate because it has 1 (a unit) in the denominator.

4a, 4b, ... all slope calculations. You managed to get it right in problem 9. Watch your signs.

10, 11 ... It can work well to put the x term on the same side with the y-term, then multiply the equation by the denominator value.

... (2/3)x + y = 7 . . . . add (2/3)x to both sides of the equation

... 2x + 3y = 21 . . . . . multiply by 3. (Standard form always has the leading coefficient positive.)

Whenever you consider making a term disappear from one side of the equation, think in terms of adding its opposite to both sides of the equation. This will give the result you want and is consistent with the properties of equality: whatever you do to one side of the equation you must also do to the other side of the equation. Other wording may have been used by your teacher or friends. This is the one true statement about transforming equations.

Mathematics

15 points can someone check my answers? 1. for the data in the table, does y vary directly with x? if it does write an equation for the direct variation.(x,y) (8,11) (16,22) (24,33) yes y=2.75x yes y=0.6875x*** yes y=1.375x no y does not vary directly with x ** (for #1, i m debating between b and d) 2.for the data in the table, does y vary directly with x? if it does write an equation for the direct variation. (x,y) (16,4) (32,16) (48,36) yes y=2x yes y=4x yes y=8x no y does not very directly with x*** 3. (time/hour,distance/miles)(4,233) (6,348)

Step-by-step answer

P Answered by PhD

12

1. y varies directly with x and the equation is y=1.375x

2. No, y does not vary directly with x

3. Your car travels 58 miles in 1 hour

4. $-\frac{1}{3}$

4.

5. $-\frac{26}{27}$

6. y-2=3(x-5)

7. $y+5=-\frac{2}{5}(x+3)$

8. y+7=-0.54(x-4)

9. y-16=8(x-2)

10. 2x+3y=21

11. x+2y=2

Step-by-step explanation:

1.

For to vary directly with , all the 3 pair of numbers need to show the same ratio if we divide each y's by the x's. Let's check.

$\frac{11}{8}=1.375$ $\frac{22}{16}=1.375$ $\frac{33}{24}=1.375$

So all of them show the same ratio and hence y varies directly with x.

For equation, we already saw that multiplying x by 1.375 gives us y. We can write in equation form as:

y=1.375x

Third answer choice is correct.

2.

This is similar to #1. So let's check the ratios.

$\frac{4}{16}=0.25$ $\frac{16}{32}=0.5$ $\frac{36}{48}=0.75$

As we can see, the ratios are not equal to y does not vary directly with x.

Fourth answer choice is correct.

3.

The first number in the pair gives time and second number gives distance. To get unit rate, we divide the distance by time. So we will get the number of miles traveled in 1 hour.

$\frac{233}{4}=58.25$ [ i believe this is a typo and it should be 232 miles and ratio would be 58 ]

$\frac{348}{6}=58$

$\frac{464}{8}=58$

$\frac{580}{10}=58$

As we can see, in 1 hour, distance covered is 58 miles. Third answer choice is right.

4.

If the 2 points are taken as $(x_{1},y_{1})$ and $(x_{2},y_{2})$

And we know formula of slope to be:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of the line is:

$\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}$

The slope of the line is $-\frac{1}{3}$

Second answer choice is correct.

4. [this should be #5]

If the 2 points are taken as $(x_{1},y_{1})$ and $(x_{2},y_{2})$

And we know formula of slope to be:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of this line can be found now:

$\frac{2.7-8.7}{-3.2-(-5.2)}=\frac{2.7-8.7}{-3.2+5.2}=\frac{-6}{2}=-3$

The slope of the line is

Fourth answer choice is correct.

5.

The formula of slope is:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where,

the 2 points are taken as $(x_{1},y_{1})$ and $(x_{2},y_{2})$

Now finding the slope:

$\frac{\frac{7}{3}-(-2)}{-3-\frac{3}{2}}=\frac{\frac{7}{3}+2}{-\frac{9}{2}}=\frac{\frac{13}{3}}{-\frac{9}{2}}=-\frac{26}{27}$

The slope of the line is $-\frac{26}{27}$

Second answer choice is right.

6.

Point Slope form of a line is given as:

$y-y_{1}=m(x-x_{1})$

Where,

$(x_{1},y_{1})$ is the point given, andm is the slope

Using the point (5, 2) and slope as 3 given, we can write the equation:

y-2=3(x-5)

Fourth answer choice is right.

7.

Point Slope form of a line is given as:

$y-y_{1}=m(x-x_{1})$

Where,

$(x_{1},y_{1})$ is the point given, andm is the slope

Using the point given as (-3,-5) and slope as $m=-\frac{2}{5}$ , we can write the point slope form of the equation as:

$y-(-5)=-\frac{2}{5}(x-(-3))\\y+5=-\frac{2}{5}(x+3)$

First answer choice is right.

8.

Point Slope form of a line is given as:

$y-y_{1}=m(x-x_{1})$

Where,

$(x_{1},y_{1})$ is the point given, andm is the slope

The slope is given as -0.54 and the point is (4, -7). So the point slope form is:

$y-(-7)=-0.54(x-4)\\y+7=-0.54(x-4)$

First answer choice is right.

9.

In this question, we can just have a quick look and see that the -coordinate is 8 times the -coordinate. So we can say that y=8x

Expanding the equations below would tell us which one is equal to that. Let's check.

$y-16=8(x-2)\\y-16=8x-16\\y=8x-16+16\\y=8x$

This is the correct one.

So first answer choice is right.

10.

The standard form of the equation of a line is given as:

Ax+By=C

Rearranging the given equation gives us:

$y=-\frac{2}{3}x+7\\\frac{2}{3}x+y=7$

Now, we can't have a fraction, so we multiply all of it by 3 to get rid of the denominator. Now we have:

$3*(\frac{2}{3}x+y=7)\\2x+3y=21$

First answer choice is right.

11.

The standard form of a line is Ax+By=C

Rearranging the given equation, we have:

$y=-\frac{1}{2}x+1\\\frac{1}{2}x+y=1$

We cannot have fractions, so we multiply the whole thing by 2 to get rid of the denominator. So we have:

$2*(\frac{1}{2}x+y=1)\\x+2y=2$

First answer choice is correct.

Mathematics

1) write the standard form of an equation of the line that passes through (3, 5) and has a slope of -3/4. not enough information 3/4x+y=29/4 3x+4y=29 y = -3/4x +29/4 2) write the point-slope form of an equation for a vertical line that passes through (-4, -7). 0 = x + 7 0 = x - 4 0 = x + 4 0 = x - 7 3) write the slope-intercept form of equation of the line that passes through (-2, 3) and has a slope of m = -3. 3x+y = 9 3x+y = -9 y = 3x+9 y = -3x-3 4) write the point-slope form of an equation for a horizontal line that passes through (-15, 11).

Step-by-step answer

P Answered by Specialist

7

◆ Straight Lines ◆

[ 1 ]

Any equation with a slope m can be expressed in the form of :

y = mx + c

Here m = -3/4 ;
Line is passing through (3,5)

Substituting in std. equation ,

5 = -3/4(3) + c
---> 5 = -9/4 + c
---> c = 5 + 9/4 = 29/4

Hence ,

Equation of line is :-

y = -3x/4 + 29/4 Ans.

[ 2 ]

Line is passing through ( -4 , -7 )

Therefore x = -4 ; y = -7

+ It's a vertical line

Hence , equation of line -
x + 4 = 0 Ans.

[ 3 ]

Any equation with a slope m can be expressed in the form of :

y = mx + c

Here m = -3 ;
Line is passing through ( -2 , 3 )

Substituting in std. equation ,

3 = -3(-2) + c
---> 3 = 6 + c
---> c = -3

Hence ,

Equation of line is :-

y = -3x - 3

[ 4 ]

Line is passing through ( -15 , 11 )

Therefore x = -15 ; y = 11

+ It's a Horizontal line

Hence , equation of line -
y - 11 = 0 Ans.

Hope it helps you :)

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Mathematics

1) write the standard form of an equation of the line that passes through (3, 5) and has a slope of -3/4. not enough information 3/4x+y=29/4 3x+4y=29 y = -3/4x +29/4 2) write the point-slope form of an equation for a vertical line that passes through (-4, -7). 0 = x + 7 0 = x - 4 0 = x + 4 0 = x - 7 3) write the slope-intercept form of equation of the line that passes through (-2, 3) and has a slope of m = -3. 3x+y = 9 3x+y = -9 y = 3x+9 y = -3x-3 4) write the point-slope form of an equation for a horizontal line that passes through (-15, 11).

Step-by-step answer

P Answered by Specialist

7

◆ Straight Lines ◆

[ 1 ]

Any equation with a slope m can be expressed in the form of :

y = mx + c

Here m = -3/4 ;
Line is passing through (3,5)

Substituting in std. equation ,

5 = -3/4(3) + c
---> 5 = -9/4 + c
---> c = 5 + 9/4 = 29/4

Hence ,

Equation of line is :-

y = -3x/4 + 29/4 Ans.

[ 2 ]

Line is passing through ( -4 , -7 )

Therefore x = -4 ; y = -7

+ It's a vertical line

Hence , equation of line -
x + 4 = 0 Ans.

[ 3 ]

Any equation with a slope m can be expressed in the form of :

y = mx + c

Here m = -3 ;
Line is passing through ( -2 , 3 )

Substituting in std. equation ,

3 = -3(-2) + c
---> 3 = 6 + c
---> c = -3

Hence ,

Equation of line is :-

y = -3x - 3

[ 4 ]

Line is passing through ( -15 , 11 )

Therefore x = -15 ; y = 11

+ It's a Horizontal line

Hence , equation of line -
y - 11 = 0 Ans.

Hope it helps you :)

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Mathematics

Find the distance between (3, 8) and (7, -11). round to the nearest hundredth. find the coordinates of the midpoint of jk if j (-9, 5) and k(21, -7). find the coordinates of the midpoint of ab if a(-8, 7) and b(-9, 11). if the midpoint between (8, y) and (-11, 6) is (-1.5, 5), find the value of y. find the slope of the line that passes through the points (3, -6) and (6, 12). find the value of x so that the line passing through (x, 10) and (-4, 8) has a slope of 2/3 find the value of y so that the line passing through (9, 0) and (3, y) has a slope

Step-by-step answer

P Answered by PhD

3

The answers are;

The distance between (3,8)

and

is $19.42\text{ (to the nearest hundredth)}$ The midpoint of the line

is

The midpoint of the line

is

The value of

is

The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

The value of

is

The value of

is $-\frac{3}{2}$ The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

In coordinate geometry, given two points (x_1,y_1) and (x_2,y_2) ;

The distance between them is given by $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ The midpoint has the coordinates $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ The slope of the line passing through the points is the ratio $\frac{y_2-y_1}{x_2-x_1}$

These formulae will be used to solve the following problems:

1) Given points (3,8) and (7,-11) , the distance between them is

$\sqrt{(7-3)^2+(-11-8)^2}\approx 19.42 \text{ (to the nearest hundredth)}$