Answer:
[tex]y = -\frac{1}{4}x +2[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Given points: (-4, 3), (0, 2)
(0, 2) = (x1, y1)
(-4, 3) = (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 formula used to find slope:
[tex]\frac{3-2}{-4-0}[/tex]
Simplify:
3 - 2 = 1
-4 - 0 = -4
[tex]\frac{1}{-4}= -\frac{1}{4}[/tex]
The slope is [tex]-\frac{1}{4}[/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{1}{4} (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{1}{4}x +2[/tex]
