Question

1. Find the equations of the following lines.

Answer 1

Answer:

$y = -\frac{1}{4}x + \frac{3}{4}$

Step-by-step explanation:

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

slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Let:

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

Plug in the corresponding numbers to the corresponding variables:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{3 - (-1)} = \frac{-1}{3 + 1} = -\frac{1}{4}$

Plug in $-\frac{1}{4}$ into the equation for slope:

y = mx + b

Note that:

y = y

m = slope

x = x

b = y-intercept

$y = -\frac{1}{4}x + b$

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

$0 = -\frac{1}{4}(3) + b \\0 = -\frac{1 * 3}{4} + b\\0 = -\frac{3}{4} + b\\0 (+\frac{3}{4}) = -\frac{3}{4} (+\frac{3}{4}) + b\\b = \frac{3}{4}$

Equation:

$y = -\frac{1}{4}x + \frac{3}{4}$