Question

In slope intercept form line that goes through (3,10) (6,8)

Another one
Through(2,-10) (-4,2)

Please help with these two

Answer 1

`y= -(2)/(3)x + 12` --- (1)

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

Explanation:

Solving (a): Line Equation

`(x_1,y_1) = (3,10)`

`(x_2,y_2) = (6,8)`

First, calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (8 - 10)/(6 -3)`

`m = (-2)/(3)`

`m = -(2)/(3)`

The line equation is then calculated using:

`y - y_1 = m(x - x_1)` --- slope intercept formula

This gives:

`y - 10 = -(2)/(3)(x - 3)`

`y - 10 = -(2)/(3)x + 2`

Solve for y

`y= -(2)/(3)x + 2+10`

`y= -(2)/(3)x + 12`

Solving (b): Line Equation

`(x_1,y_1) = (2,-10)`

`(x_2,y_2) = (-4,2)`

Calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (2 -(- 10))/(-4 -2)`

`m = (2 + 10)/(-6)`

`m = (12)/(-6)`

`m=-2`

The line equation is then calculated using:

`y - y_1 = m(x - x_1)`

This gives:

`y - (-10) = -2(x - 2)`

`y +10 = -2(x - 2)`

`y +10 = -2x +4`

Solve for y

`y = -2x +4-10`

`y = -2x -6`