Answer:
[tex]y=\frac{1}{2}x[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Given points: (2, 1), (-4, -2)
(2, 1) = (x1, y1)
(-4, -2) = (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{-2-1}{-4-2}[/tex]
Simplify:
-2 - 1 = -3
-4 - 2 = -6
[tex]\frac{-3}{-6} =\frac{1}{2}[/tex]
The slope is [tex]\frac{1}{2}[/tex]. We can input the slope and one of the given points (in this example I'll use point (2, 1)) into the equation to find b:
[tex]1= \frac{1}{2}(2)+b[/tex]
1 = 1 + b
0 = b
The y-intercept is 0. Now that we know the slope and the y-intercept, we can write the equation:
[tex]y = \frac{1}{2}x+0[/tex]
[tex]y=\frac{1}{2}x[/tex]
