What is the y-intercept of each equation? y=6x+2 and the equation 10x+5y=30? explain.

Part 1)

we know that

the equation of the line in slope-intercept form is equal to

where

m is the slope

b is the y-intercept

we have

solve for y

-------> equation of the line in slope-intercept form

so

the slope m  is

the y-intercept b is

Part 2)

we know that

the equation of the line in slope-intercept form is equal to

where

m is the slope

b is the y-intercept

we have

solve for y

-------> equation of the line in slope-intercept form

so

the slope m  is

the y-intercept b is

Part 3)

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

we have

a) Find the x-intercept

For substitute in the equation

The answer part 3a) is

b) Find the y-intercept

For substitute in the equation

The answer part 3b) is

Part 4)

we know that

the equation of the line in standard form is

we have

Multiply by both sides

------> equation in standard form

therefore

the answer Part 4) is option B False

Part 5)

Step 1

Find the slope

we have

solve for y

so

the slope m is

Step 2

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

we have

for

the y-intercept is

Step 3

Find the equation of the line

we have

the equation of the line in slope-intercept form is

substitute the values

therefore

the answer Part 5) is the option A

Part 6)

Step 1

Find the slope of the given line

we know that

if two lines are perpendicular. then the product of their slopes is equal to minus one

so

in this problem

the given line

solve for y

the slope m1 is

so

the slope m2 is

Step 2

Find the equation of the line

we know that

the equation of the line in slope point form is equal to

we have

point

substitutes the values

therefore

the answer part 6) is the option C

Part 7)

 -------> the slope is

--------> the slope is

we know that

if two lines are parallel , then their slopes are the same

in this problem the slopes are not the same

therefore

the answer part 7) is the option D) No, since the slopes are different.

Part 8)

a. Write an equation for the line in point-slope form

b. Rewrite the equation in standard form using integers

Step 1

Find the slope of the line

we know that

the slope between two points is equal to

substitute the values

Step 2

Find the equation in point slope form

we know that

the equation of the line in slope point form is equal to

we have

point

substitutes the values

-------> equation of the line in point slope form

Step 3

Rewrite the equation in standard form using integers

Multiply by both sides

--------> equation of the line in standard form

Part 9)

we know that

The formula to calculate the slope between two points is equal to

where

(x1,y1) ------> is the first point

(x2,y2) -----> is the second point

In the numerator calculate the difference of the y-coordinates

in the denominator calculate the difference of the x-coordinates

Part 10)

we know that

The formula to calculate the slope between two points is equal to

substitutes

therefore

the answer Part 10) is

Part 11)

we know that

the equation of the line in slope point form is equal to

substitute the values

--------> this is the equation in the point slope form

A because they create parallel lines but only have different intercepts.

A because they create parallel lines but only have different intercepts.

D.)  "The graphs of the equations intersect each other at two places."

D.)  "The graphs of the equations intersect each other at two places."

A.

B.

Step-by-step explanation:

I think this is what you were looking for.

A.

B.

Step-by-step explanation:

I think this is what you were looking for.

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

2b. y + 2 = −⅔(x + 3)

2a. y - 3 = ⅘(x - 5)

1b. y = -x + 5

1a. y = 5x - 3

Step-by-step explanation:

4.

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

b.

2 = 6[1] + b

6

−4 = b

y = 6x - 4

-6x - 6x

−6x + y = −4 >> Standard Equation

a.

4 = −7⁄4[-4] + b

7

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

3.

Plug both coordinates into the Slope-Intercept Formula:

b.

5 = ½[4] + b

2

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

a.

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR RATE OF CHANGES [SLOPES].

2.

b. y + 2 = −⅔(x + 3)

a. y - 3 = ⅘(x - 5)

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

1.

b. y = -x + 5

a. y = 5x - 3

Just write out the Slope-Intercept Formula as it is given to you.

I am joyous to assist you anytime.

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

2b. y + 2 = −⅔(x + 3)

2a. y - 3 = ⅘(x - 5)

1b. y = -x + 5

1a. y = 5x - 3

Step-by-step explanation:

4.

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

b.

2 = 6[1] + b

6

−4 = b

y = 6x - 4

-6x - 6x

−6x + y = −4 >> Standard Equation

a.

4 = −7⁄4[-4] + b

7

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

3.

Plug both coordinates into the Slope-Intercept Formula:

b.

5 = ½[4] + b

2

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

a.

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR RATE OF CHANGES [SLOPES].

2.

b. y + 2 = −⅔(x + 3)

a. y - 3 = ⅘(x - 5)

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

1.

b. y = -x + 5

a. y = 5x - 3

Just write out the Slope-Intercept Formula as it is given to you.

I am joyous to assist you anytime.