Answer:
The equation for the following graph:
[tex]y = -\frac{1}{5}x[/tex]
Step-by-step explanation:
- You first need to find the slope by using the slope formula:
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
(where [tex](x_{1},y_{1})[/tex] is the first point and [tex](x_{2}, y_{2})[/tex] is the second point)
-Use the given points [tex](0,0)[/tex] and [tex](10, -2)[/tex] from the graph for the formula:
[tex]m = \frac{-2 - 0}{10 - 0}[/tex]
Then, you solve:
[tex]m = \frac{-2 - 0}{10 - 0}[/tex]
[tex]m = -\frac{1}{5}[/tex]
After you have found the slope, use the slope [tex]-\frac{1}{5}[/tex] and the first point [tex](0,0)[/tex] for the point-slope formula:
[tex]y - y_{1} = m ( x - x_{1})[/tex]
(where [tex]m[/tex] is the slope and [tex](x_{1}, y_{1})[/tex] is the first point)
[tex]y - 0 = -\frac{1}{5} ( x - 0)[/tex]
Then, you solve:
[tex]y - 0 = -\frac{1}{5} ( x - 0)[/tex]
[tex]y - 0 = -\frac{1}{5}x - 0[/tex]
[tex]y - 0 + 0 = -\frac{1}{5} - 0 + 0[/tex]
[tex]y = -\frac{1}{5}x[/tex]
So, the equation for the following graph is [tex]y = -\frac{1}{5}x[/tex] .
