Question

Write an equation of the line in slope-intercept form.

y=

Answer 1

$\huge\boxed{y=-\frac{4}{3}}$

To find the equation for a line in slope-intercept form, we need to find the slope and the y-intercept.

The y-intercept is easy to find. It's just the value of $x$ when $y=0$. In this case, the y-intercept is $0$ since the line goes through the origin.

To find the slope, we use the slope formula, where $(x_1, y_1)$ and $(x_2, y_2)$ are two known points. In this case, we'll use the only two points we have: $(0, 0)$ and $(-3, 4)$

$\begin{aligned}m&=\frac{y_2-y_1}{x_2-x_1}\\&=\frac{4-0}{-3-0}\\&=\frac{4}{-3}\\&=-\frac{4}{3}\end{aligned}$

Finally, we put it all together in slope-intercept form, where $m$ is the slope and $b$ is the y-intercept.

$y=mx+b\\y=-\dfrac{4}{3}x+0\\\boxed{y=-\frac{4}{3}}$