Explanation
- Calculate the slope by using the rise over run with two given coordinate points.
Note: Origin point = (0,0).
[tex] \begin{cases}(x_1, y_1) = ( - 4, - 9) \\ (x_2, y_2) = ( 0, 0) \end{cases}[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{0 - ( - 9)}{0 - ( - 4)} \\ m = \frac{0 + 9}{0 + 4} \Longrightarrow \frac{9}{4} [/tex]
[tex]y = mx + b \\ \begin{cases} \sf{m = slope} \\ \sf{b = y - intercept} \end{cases}[/tex]
Rewrite the equation by substituting m = 9/4 in the equation.
[tex]y = \frac{9}{4} x + b[/tex]
Because the graph passes through the origin point. That means the y-intercept is (0,0).
Therefore we rewrite the equation again to
[tex]y = \frac{9}{4} x + 0 \\ y = \frac{9}{4} x[/tex]
Answer
[tex] \large \boxed{y = \frac{9}{4} x}[/tex]
