Answer:
[tex]y=-\frac{3}{2}x-2[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Given points: (0, -2), (-4, 4)
(0, -2) = (x1, y1)
(-4, 4) = (x2, y2)
To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.
First, let's find the slope. To do this, input the given points into the slope formula:
[tex]\frac{4-(-2)}{-4-0}[/tex]
Simplify:
4 - (-2) = 4 + 2 = 6
-4 - 0 = -4
[tex]\frac{6}{-4}=-\frac{3}{2}[/tex]
The slope is [tex]-\frac{3}{2}[/tex].
To find the y-intercept, input the slope and one of the given points(in this example I'll use point (0, -2)) into the equation and solve for b:
[tex]-2 = -\frac{3}{2}(0)+b[/tex]
-2 = 0 + b
-2 = b
The y-intercept is -2.
Now that we know the slope and the y-intercept, we can write the equation:
[tex]y=-\frac{3}{2}x-2[/tex]
