A line with slope = 2/3 contains the point (-4, 5). Using the slope, what are two more points on that line?

Jun 14, 2018

$\left(0 , \frac{23}{3}\right)$ etc.

Explanation:

First solve the equation for the line:

Use the Point Slope form of a line:

$\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{g r e e n}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$\left(y - \textcolor{b l u e}{5}\right) = \textcolor{g r e e n}{\frac{2}{3}} \left(x - \textcolor{b l u e}{\left(- 4\right)}\right)$

$\left(y - \textcolor{b l u e}{5}\right) = \textcolor{g r e e n}{\frac{2}{3}} \left(x + \textcolor{b l u e}{4}\right)$

$y - 5 = \frac{2}{3} x + \frac{8}{3}$

$y = \frac{2}{3} x + \frac{8}{3} + 5$

$y = \frac{2}{3} x + \frac{8}{3} + \frac{15}{3}$

$y = \frac{2}{3} x + \frac{8}{3} + \frac{15}{3}$

$y = \frac{2}{3} x + \frac{23}{3}$

Now plug any values for x in to solve for y for example:

$x = 0$ then $y = \frac{23}{3}$

$\left(0 , \frac{23}{3}\right)$ etc.