[tex]y = -\frac{1}{2}x - 1[/tex]
Step-by-step explanation:
Let's pick two points on the line: [tex]P_1(-4, 1)[/tex] and [tex]P_2(2, -2).[/tex] Let's calculate the slope of this line using these points:
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-2 - 1}{2 - (-4)} = -\dfrac{1}{2}[/tex]
With this value of the slope, we can write the general slope-intercept form of the equation as
[tex]y = -\frac{1}{2}x + b[/tex]
To solve for the y-intercept b, let's use either P1 or P2. I'm going to use P2:
[tex]-2 = -\frac{1}{2}(2) + b \Rightarrow b = -1[/tex]
Therefore, the slope-intercept form of the equation is
[tex]y = -\frac{1}{2}x - 1[/tex]
