Question

1. Find the equations of the following lines.

a. The line that passes through points A(-1,1) and B(3,0).​

Answer 1

`y = -(1)/(4)x + (3)/(4)`

Explanation:

First, find the slope. The slope can be found by using the following equation:

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

Let:

`(x_1 , y_1) = (-1 , 1)\\(x_2 , y_2) = (3 , 0)`

Plug in the corresponding numbers to the corresponding variables:

`m = (y_2 - y_1)/(x_2 - x_1) = (0 - 1)/(3 - (-1)) = (-1)/(3 + 1) = -(1)/(4)`

Plug in
`-(1)/(4)` into the equation for slope:

y = mx + b

Note that:

y = y

m = slope

x = x

b = y-intercept

`y = -(1)/(4)x + b`

Plug in a point into the equation. In this case, I will use b(3 , 0). Remember (x , y):

`0 = -(1)/(4)(3) + b \\0 = -(1 * 3)/(4) + b\\0 = -(3)/(4) + b\\0 (+(3)/(4)) = -(3)/(4) (+(3)/(4)) + b\\b = (3)/(4)`

Equation:

`y = -(1)/(4)x + (3)/(4)`