Note: It seems you forgot to attach the table diagram. After a little research, I am able to find a table which is attached below.
Answer:
we conclude that:
- The y-intercept = b = -1/3
Step-by-step explanation:
Finding the slope
Taking two points from the given table (check the attached diagram)
Finding the slope between (-3/4, -1/30) and (-1/2, -2/15)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{\frac{-2}{15}-\frac{-1}{30}}{\frac{-1}{2}-\frac{-3}{4}}[/tex]
[tex]m=-\frac{2}{5}[/tex]
Finding the y-intercept
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Given
- [tex]m=-\frac{2}{5}[/tex]
substitute to find the y-intercept (b)
[tex]y=mx+b[/tex]
[tex]\left(\frac{-1}{30}\right)=-\frac{2}{5}\left(\frac{-3}{4}\right)+b[/tex]
switch sides
[tex]-\frac{2}{5}\left(\frac{-3}{4}\right)+b=\left(\frac{-1}{30}\right)[/tex]
[tex]\frac{3}{10}+b=\left(\frac{-1}{30}\right)[/tex]
[tex]\mathrm{Subtract\:}\frac{3}{10}\mathrm{\:from\:both\:sides}[/tex]
[tex]\frac{3}{10}+b-\frac{3}{10}=\frac{-1}{30}-\frac{3}{10}[/tex]
[tex]b=-\frac{1}{3}[/tex]
Therefore, we conclude that:
- The y-intercept = b = -1/3
