Question

Write the equation of a line in slope-intercept form that goes through the points

Answer 1

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

To find the slope(m), use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$    And plug in the two points on the line

(-4, -4) = (x₁, y₁)

(4, -2) = (x₂, y₂)

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

$m=\frac{-2-(-4)}{4-(-4)}$ (two negative signs cancel each other out and become positive)

$m=\frac{-2+4}{4+4}$

$m=\frac{2}{8}$     Simplify the fraction

$m=\frac{1}{4}$      Now that you know the slope, substitute/plug it into the equation

y = mx + b

$y=\frac{1}{4} x+b$  To find b, plug in either of the points into the equation, it doesn't matter which, then isolate/get the variable "b" by itself. I will use (4, -2)

$-2=\frac{1}{4}(4)+b$

-2 = 1 + b    Subtract 1 on both sides to get "b" by itself

-3 = b

$y=\frac{1}{4} x-3$  Your answer is A