Answer: the second option is correct [tex](0. -\frac{4}{3} ) (2, 0 )[/tex]
Using Slope = rise/run . [tex]y=\frac{2}{3}x\ -\frac{4}{3}[/tex]
You can create a graph to see the intercepts (attached) OR
Step-by-step explanation:
To find the y-intercept, figure half way between (-1, -2) and (1, 2/3)
[tex]\frac{2}{3} -(-2) = 2\frac{2}{3}[/tex] Half of that is [tex]1\frac{1}{3}[/tex] below the origin, y-intercept is [tex]-1 \frac{1}{3}[/tex] or [tex]-\frac{4}{3}[/tex]
to create an equation for this:
Take the difference in y-values [tex]\frac{2}{3} -(-\frac{10}{3} ) = 12/3[/tex]
which simplifies to 4 for the Rise
Take the difference in x-values [tex]3 -(-3) = 6[/tex]
so the Run is 6
The slope is the slope is 4/6 , the same as 2/3.
Use slope intercept form to create the equation:
[tex]y=\frac{2}{3}x\ -\frac{4}{3}[/tex]
You can compute the x-intercept by substituting 0 for y
0 = 2x/3 - 4/3 . 4/3 = 2x/3 multiply both sides by 3
4 = 2x divies both sides by 2 to get 2 = x, the x-intercept
