How do you find the x and y intercept given (-6, 2) and (-3, 4)?

Nov 10, 2015

x-intercept: $\left(- 9\right)$
y-intercept: $6$

Explanation:

Assuming the equation form we are looking for is linear
then the slope is constant

Slope between the general point $\left(x , y\right)$ and $\left(- 6 , 2\right)$ is the same as between $\left(- 3 , 4\right)$ and $\left(- 6 , 2\right)$

$\frac{y - 2}{x + 6} = \frac{4 - 2}{- 3 + 6} = \frac{2}{3}$

$\Rightarrow 3 \left(y - 2\right) = 2 \left(x + 6\right)$

$\Rightarrow 3 y - 6 = 2 x + 12$

$\Rightarrow 3 y = 2 x + 18$

When $y = 0$ (the x-intercept) $3 \left(0\right) = 2 x + 18 \rightarrow x = - 9$

When $x = 0$ (the y-intercept) $3 y = 2 \left(x\right) + 18 \rightarrow y = 6$