Question

PLEASE HELP MEEEE 28 POINTS!!!!

A. Find an equation in​ point-slope form for the line having the slope m = 6 and containing the points (7,2)
B. Find an equation in​ point-slope form for the line having the slope m=-4 and containing the point ​(​1,9​).

Answer 1

The answer is:

1) y - 2 = 6(x - 7)

2) y - 9 = -4(x - 1)

Work/explanation:

The point slope formula is:

`\bf{y-y_1=m(x-x_1)}`

where m = slope;

(x₁, y₁) is a point on the line.

For this problem, m = 6 and the point is (7,2).

Plug in the data:

`\bf{y-2=6(x-7)}`

__________________

For this problem, m = -4 and the point is (1,9).

Plug in the data:

`\bf{y-9=-4(x-1)}`

Hence, these are the equations.

Answer 2

Part A)

An equation in​ point-slope form for the line having the slope m = 6 and containing the point (7,2).

`y - 2 = 6(x-7)`

Part B)

An equation in​ point-slope form for the line having the slope m = -4 and containing the point (1, 9).

`y - 9 = -4(x-1)`

Explanation:

Part A)

Given

Slope m = 6

Point (7, 2)

To Determine

Find an equation in​ point-slope form for the line having the slope m = 6 and containing the point (7,2).

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

In our case:

• m = 6

• (x₁, y₁) = (7, 2)

substituting the values m = 6 and the point (x₁, y₁) = (7, 2) in the point-slope form of line equation

`y-y_1=m\left(x-x_1\right)`

`y - 2 = 6(x-7)`

Therefore, an equation in​ point-slope form for the line having the slope m = 6 and containing the point (7,2).

`y - 2 = 6(x-7)`

Part B)

Given

Slope m = -4

Point (1, 9)

To Determine

Find an equation in​ point-slope form for the line having the slope m = -4 and containing the point (1, 9).

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

In our case:

• m = -4

• (x₁, y₁) = (1, 9)

substituting the values m = -4 and the point (x₁, y₁) = (1, 9) in the point-slope form of line equation

`y-y_1=m\left(x-x_1\right)`

`y - 9 = -4(x-1)`

Therefore, an equation in​ point-slope form for the line having the slope m = -4 and containing the point (1, 9).

`y - 9 = -4(x-1)`