Question

Write the equation, in slope-intercept form, of the line passing through the origin and the point $(-4,3)$.

Answer 1

If the equation is passing trough the origin, it will be passing trough the point (0,0). We now for our problem that the equations is also passing trough the point (-4,3). So, our line is passing trough the points (0,0) and (-4,3). To write the equation in slope-intercept form, first, we need to find its slope $m$. To do that we are going to use the slope formula: $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.
From our two points we can infer that $x_{1}=0$, $y_{1}=0$, $x_{2}=-4$, $y_{2}=3$. Lets replace those values in the slope formula:
$m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m= \frac{3-0}{-4-0}$
$m= \frac{3}{-4}$
$m=- \frac{3}{4}$

Now that we have our slope, we can use the slope-intercept formula:
$y-y_{1}=m(x-x_{1})$
$y-0=- \frac{3}{4} (x-0)$
$y=- \frac{3}{4} x$

We can conclude that the equation of the line passing trough the points (0,0) and (-4,3) is $y=- \frac{3}{4} x$.