Answer:
E. [tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
Take the two points shown:
[tex](0,0)(6,2)[/tex]
Use these to make an equation in slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept (where x is equal to 0).
Use the slope formula:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert coordinate points:
[tex](0_{x1},0_{y1})\\\\(6_{x2},2_{y2})\\\\\frac{2-0}{6-0}[/tex]
Simplify:
[tex]\frac{2-0}{6-0} =\frac{2}{6} =\frac{1}{3}[/tex]
The slope is [tex]\frac{1}{3}[/tex]. Insert this into the equation:
[tex]y=\frac{1}{3}x+b[/tex]
Now find the y-intercept. Take one of the coordinate points and insert:
[tex](6_{x},2_{y})\\\\2=\frac{1}{3}(6)+b[/tex]
Solve for b. Simplify multiplication:
[tex]\frac{1}{3}*\frac{6}{1}=\frac{6}{3}=2\\\\ 2=2+b[/tex]
Use reverse operations to isolate the variable:
[tex]2-2=2-2+b\\\\0=b[/tex]
The y-intercept is equal to 0. Insert this into the equation:
[tex]y=\frac{1}{3}x+0[/tex]
or
[tex]y=\frac{1}{3}x[/tex]
:Done
