Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

$y = -\frac{1}{2}x - 1$

Step-by-step explanation:

Let's pick two points on the line: $P_1(-4, 1)$ and $P_2(2, -2).$ Let's calculate the slope of this line using these points:

$m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-2 - 1}{2 - (-4)} = -\dfrac{1}{2}$

With this value of the slope, we can write the general slope-intercept form of the equation as

$y = -\frac{1}{2}x + b$

To solve for the y-intercept b, let's use either P1 or P2. I'm going to use P2:

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

Therefore, the slope-intercept form of the equation is

$y = -\frac{1}{2}x - 1$