Question

Find the equation of the line with a y-intercept of -3 and a x-intercept of -4.5

Answer 1

So with intercepts, we know that one of the coordinates is 0 - that is because the line intercepts the axis at this point.

When we have a y-intercept of -3, it is written as (0,-3)

And when we have an x-intercept of -4.5, we write it as (-4.5,0)

So now we have our two points - let's find the slope using the equation:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ ---> $\frac{0-(-3)}{-4.5-0}=\frac{3}{-4.5}$

If we convert -4.5 to an improper fraction, we get:

$-4\frac{1}{2}=-\frac{9}{2}$

So then we go back and simplify:

$\frac{3}{-\frac{9}{2}}=3*-\frac{2}{9} =\frac{-6}{9}=-\frac{2}{3}$

So now we have our slope: $-\frac{2}{3}$. Then we can write the equation:

$y=-\frac{2}{3}x+b$

Let's use the point (0,-3) to solve for b:

$-3=-\frac{2}{3}(0)+b$

$b=-3$

So now we can write the equation:

$y=-\frac{2}{3} x-3$

This is the equation of the line with points (0,-3) and (-4.5,0).