Find the equation of the line from given point, №18010742, 21.01.2023 08:13

Mathematics

Find the equation of the line from given point and slope a) passes through (-5,4) and has slope, m=1/2

Step-by-step answer

P Answered by Master

Slope-intercept form:

$y=\dfrac12x+\dfrac{13}2$

Standard form:

x-2y=-13

Step-by-step explanation:

Point-slope form of a linear equation: y-y_1=m(x-x_1)

(where is the slope and (x_1,y_1) is the point)

Given:

$m=\dfrac12$ (x_1,y_1)=(-5,4)

Substituting these values into the point-slope formula:

$\implies y-4=\dfrac12(x+5)$

$\implies y-4=\dfrac12x+\dfrac52$

$\implies y=\dfrac12x+\dfrac{13}2$

Slope-intercept form:

$y=\dfrac12x+\dfrac{13}2$

Standard form:

x-2y=-13

Mathematics

Given 8y — 6x =8 : a) transform the equation into slope-intercept form. b) find the slope and y-intercept of the line. c) what is the slope of a line parallel to this line? d) what is the slope of a line perpendicular to this line ? e) find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point (0,2).

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

A: slope-intercept form: Solve 8y — 6x =8 for y, as follows: 8y = 6x + 8, so that y = (3/4)x + 1.

B: Slope: 3/4; y-intercept: (0, 1)

C: Any line parallel to this line has the same slope, namely, 3/4.

D: Any line perpendicular to this line has a slope that is the negative reciprocal of 3/4; that is, the slope of the perp. line is -4/3.

Mathematics

Given 8y — 6x =8 : a) transform the equation into slope-intercept form. b) find the slope and y-intercept of the line. c) what is the slope of a line parallel to this line? d) what is the slope of a line perpendicular to this line ? e) find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point (0,2).

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

A: slope-intercept form: Solve 8y — 6x =8 for y, as follows: 8y = 6x + 8, so that y = (3/4)x + 1.

B: Slope: 3/4; y-intercept: (0, 1)

C: Any line parallel to this line has the same slope, namely, 3/4.

D: Any line perpendicular to this line has a slope that is the negative reciprocal of 3/4; that is, the slope of the perp. line is -4/3.

Mathematics

3. given 4x – 8y = 8: a) transform the equation into slope-intercept form. b) find the slope and y-intercept of the line. c) find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point (1, 2).

Step-by-step answer

P Answered by Specialist

16

Slope-intercept form is y = mx + b, so to turn that equation into slope-intercept you'll need to get y alone

4x - 8y = 8 --- subtract 4x
-8y = 8 - 4x --- divide by -8
y = -1 + (1/2)x --- reorder to match "mx + b"
y = (1/2)x - 1

in y = mx + b, "m" is the slope and "b" is the y-intercept. so for part B, your slope is (1/2) and your y-intercept is (-1). take the sign with you.

for part C, you'll need to know point-slope form: (y - y1) = m(x - x1)
you'll also need to be aware that "perpendicular" lines have a slope that is the opposite reciprocal of the original line.

the original slope is (1/2). change the sign to negative and form a reciprocal: your new slope is -2. plug that into your point-slope form

(y - y1) = m(x - x1)
(y - y1) = (-2)(x - x1)

and lastly, plug in your given point: (1, 2)

y - 2 = (-2)(x - 1)

so, just to look a little neater without all of the work:
A) y = (1/2)x - 1
B) m = (1/2), b = -1
C) y - 2 = (-2)(x - 1)

Mathematics

3. given 4x – 8y = 8: a) transform the equation into slope-intercept form. b) find the slope and y-intercept of the line. c) find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point (1, 2).

Step-by-step answer

P Answered by Specialist

16

Slope-intercept form is y = mx + b, so to turn that equation into slope-intercept you'll need to get y alone

4x - 8y = 8 --- subtract 4x
-8y = 8 - 4x --- divide by -8
y = -1 + (1/2)x --- reorder to match "mx + b"
y = (1/2)x - 1

in y = mx + b, "m" is the slope and "b" is the y-intercept. so for part B, your slope is (1/2) and your y-intercept is (-1). take the sign with you.

for part C, you'll need to know point-slope form: (y - y1) = m(x - x1)
you'll also need to be aware that "perpendicular" lines have a slope that is the opposite reciprocal of the original line.

the original slope is (1/2). change the sign to negative and form a reciprocal: your new slope is -2. plug that into your point-slope form

(y - y1) = m(x - x1)
(y - y1) = (-2)(x - x1)

and lastly, plug in your given point: (1, 2)

y - 2 = (-2)(x - 1)

so, just to look a little neater without all of the work:
A) y = (1/2)x - 1
B) m = (1/2), b = -1
C) y - 2 = (-2)(x - 1)

Mathematics

1. m = y2 - y1 x2 - x1 what is the slope of line segment ef? a) 1/3 b) 3/2 c) 2/3 d) 3/2 2. find the slope of the line that passes through points a and d. a) 7/2 b) 2/7 c) 0 d) 2/7 3. m = y2 - y1 x2 - x1 what is the slope of line segment jk? a) 5/9 b) 9/5 c) 5/9 d) 9/5 (4)9.determine the equation of the line given by the graph. a) y = 2x + 4 b) y = 4x + 2 c) y = 1/2 x − 2 d) y = −2x + 4 (5)10.triangle abc and triangle cfg are similar right triangles. which proportion can be used to show that the slope of ac is equal to the slope of cg? a) 0 − 2

Step-by-step answer

P Answered by PhD

5

1). Slope = $\frac{3}{2}$

2). Slope = $\frac{2}{7}$

3). Slope = $-\frac{5}{9}$

4). Option A. 2x + 4

5). Option C. $\frac{2-0}{3-0}=\frac{6-2}{9-3}$

Step-by-step explanation:

1). Slope of a line segment EF with E(-2, -4) and F(2, 2)

Slope m = $\frac{-4-2}{-2-2}$

m = $\frac{-6}{-4}$

m = $\frac{3}{2}$

2). Slope of a line segment AD with A(-3, -2) and D(4, 0)

Slope m = $\frac{-2-0}{-3-4}$

m = $\frac{2}{7}$

3). Slope of a line JK with J(-4, 2) and K(5, -3)

m = $\frac{-3-2}{5+4}$

m = $-\frac{5}{9}$

4). We have to determine the equation of the line given by graph.

In other words we have to determine the eequation of a line passing through (0, 4) and (-2, 0)

Equation will be in the form of y = mx + c

Where c = y-intercept = 4 units

Slope m = $\frac{4-0}{0+2}=(2)$

Therefore, equation of the line will be y = 2x + 4

Option A. 2x + 4 is the answer.

5). If triangles ABC and CFG are similar then AC and CG will have same slope.

Slope of AC with A(0,0) and C(3, 2) = Slope of CG with C(3, 2) and G(9, 6)

$\frac{2-0}{3-0}=\frac{6-2}{9-3}$

Therefore, Option C. is the correct option.

Mathematics

1. m = y2 - y1 x2 - x1 what is the slope of line segment ef? a) 1/3 b) 3/2 c) 2/3 d) 3/2 2. find the slope of the line that passes through points a and d. a) 7/2 b) 2/7 c) 0 d) 2/7 3. m = y2 - y1 x2 - x1 what is the slope of line segment jk? a) 5/9 b) 9/5 c) 5/9 d) 9/5 (4)9.determine the equation of the line given by the graph. a) y = 2x + 4 b) y = 4x + 2 c) y = 1/2 x − 2 d) y = −2x + 4 (5)10.triangle abc and triangle cfg are similar right triangles. which proportion can be used to show that the slope of ac is equal to the slope of cg? a) 0 − 2

Step-by-step answer

P Answered by PhD

5

1). Slope = $\frac{3}{2}$

2). Slope = $\frac{2}{7}$

3). Slope = $-\frac{5}{9}$

4). Option A. 2x + 4

5). Option C. $\frac{2-0}{3-0}=\frac{6-2}{9-3}$

Step-by-step explanation:

1). Slope of a line segment EF with E(-2, -4) and F(2, 2)

Slope m = $\frac{-4-2}{-2-2}$

m = $\frac{-6}{-4}$

m = $\frac{3}{2}$

2). Slope of a line segment AD with A(-3, -2) and D(4, 0)

Slope m = $\frac{-2-0}{-3-4}$

m = $\frac{2}{7}$

3). Slope of a line JK with J(-4, 2) and K(5, -3)

m = $\frac{-3-2}{5+4}$

m = $-\frac{5}{9}$

4). We have to determine the equation of the line given by graph.

In other words we have to determine the eequation of a line passing through (0, 4) and (-2, 0)

Equation will be in the form of y = mx + c

Where c = y-intercept = 4 units

Slope m = $\frac{4-0}{0+2}=(2)$

Therefore, equation of the line will be y = 2x + 4

Option A. 2x + 4 is the answer.

5). If triangles ABC and CFG are similar then AC and CG will have same slope.

Slope of AC with A(0,0) and C(3, 2) = Slope of CG with C(3, 2) and G(9, 6)

$\frac{2-0}{3-0}=\frac{6-2}{9-3}$

Therefore, Option C. is the correct option.

Mathematics

Suppose we are given the following. Line 1 passes through (-1, 4) and (-3, -2). Line 2 passes through (-1, -2) and (0, 1). Line 3 passes through (-6, -3) and (3, -6). (a) Find the slope of each line. Slope of Line 1 = Slope of Line 2 = 0 Slope of Line 3 = (b) For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

Step-by-step answer

P Answered by Specialist

2

Slope of line 1 = 3

Slope of line 2 = -3

Slope of line 3 = -1/3

Line 1 and 2 = perpendicular

Line 1 and 3 = perpendicular

Line 2 and 3 = perpendicular

Step-by-step explanation:

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Mathematics

Write an equation in slope-intercept form for the line that passes through the given points and is (a) parallel to the given line and (b) perpendicular to the given line. 1. (-7,3); x=4 2.(5,-1); y=4x-7

Step-by-step answer

P Answered by PhD

Remark
This is costing you an awful lot of points, but it is a little hard to read. If I'm not interpreting it correctly, leave some sort of note below my answer.

Question One
In the first question you want a line that is parallel to x = 4 and goes through the point (-7,3). If I'm reading this correctly then the line you want is x = -7. You only need the x value of the given point. I'll put a graph there to show you what it looks like on a grid. The graph is the left one for this question.

Question Two
Here I think you want the line going through (5,-1) and perpendicular to y = 4x - 7. I will make a graph for that one as well.

Begin with the slope
Two lines are perpendicular to each other if their slopes multiply to - 1
Given slope (m1) = 4
perpendicular slope = m2

Formula
m1 * m2 = - 1
4 * m2 = -1 Divide by 4
m2 = -1/4

So far what you have is
y = (-1/4)x + b

Now use the given point to solve for b
x = 5
y = - 1
b = ??

-1 = (-1/4)*5 + b
-1 = -5/4 + b Add 5/4 to both sides
-1 + 5/4 + b Make -1 into -4/4
b = -4/4 + 5/4
b = (-4 + 5)/4
b = 1/4

So the line that you want is
y = (-1/4) x + 1/4

Answers
One: x = - 7
Two: y = (-1/4)x + 1/4

Note
The right graph is of y = 4x - 7 and y = (-1/4)x + 1/4
Write an equation in slope-intercept form for the line that passes through the given points and is (

Write an equation in slope-intercept form for the line that passes through the given points and is (

Mathematics

Write an equation in slope-intercept form for the line that passes through the given points and is (a) parallel to the given line and (b) perpendicular to the given line. 1. (-7,3); x=4 2.(5,-1); y=4x-7

Step-by-step answer

P Answered by PhD

Remark
This is costing you an awful lot of points, but it is a little hard to read. If I'm not interpreting it correctly, leave some sort of note below my answer.

Question One
In the first question you want a line that is parallel to x = 4 and goes through the point (-7,3). If I'm reading this correctly then the line you want is x = -7. You only need the x value of the given point. I'll put a graph there to show you what it looks like on a grid. The graph is the left one for this question.

Question Two
Here I think you want the line going through (5,-1) and perpendicular to y = 4x - 7. I will make a graph for that one as well.

Begin with the slope
Two lines are perpendicular to each other if their slopes multiply to - 1
Given slope (m1) = 4
perpendicular slope = m2

Formula
m1 * m2 = - 1
4 * m2 = -1 Divide by 4
m2 = -1/4

So far what you have is
y = (-1/4)x + b

Now use the given point to solve for b
x = 5
y = - 1
b = ??

-1 = (-1/4)*5 + b
-1 = -5/4 + b Add 5/4 to both sides
-1 + 5/4 + b Make -1 into -4/4
b = -4/4 + 5/4
b = (-4 + 5)/4
b = 1/4

So the line that you want is
y = (-1/4) x + 1/4

Answers
One: x = - 7
Two: y = (-1/4)x + 1/4

Note
The right graph is of y = 4x - 7 and y = (-1/4)x + 1/4
Write an equation in slope-intercept form for the line that passes through the given points and is (

Find the equation of the line from given point and slope a) passes through (-5,4) and has slope, m=1/2

Step-by-step answer

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