Question

Which is an equation of the line through the origin and (-4,-9)?

Answer 1

Explanation

• Calculate the slope by using the rise over run with two given coordinate points.

Note: Origin point = (0,0).

$\begin{cases}(x_1, y_1) = ( - 4, - 9) \\ (x_2, y_2) = ( 0, 0) \end{cases}$

$m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{0 - ( - 9)}{0 - ( - 4)} \\ m = \frac{0 + 9}{0 + 4} \Longrightarrow \frac{9}{4}$

• Slope-Intercept

$y = mx + b \\ \begin{cases} \sf{m = slope} \\ \sf{b = y - intercept} \end{cases}$

Rewrite the equation by substituting m = 9/4 in the equation.

$y = \frac{9}{4} x + b$

• Find the value of b.

Because the graph passes through the origin point. That means the y-intercept is (0,0).

Therefore we rewrite the equation again to

$y = \frac{9}{4} x + 0 \\ y = \frac{9}{4} x$

Answer

$\large \boxed{y = \frac{9}{4} x}$