royalemosley
19

# What is the a line that passes through (-2,5) and has a slope of 2/3. Points A(x,3) and B(-2,y) lie on the line

Buchinski882

The point-slope form of linear equation is: $y-y_1=m(x-x_1)$ Hence, $\displaystyle y-5= \frac{2}{3}(x+2)\\\\y= \frac{2}{3}x+5 \frac{4}{3} \\\\y=\frac{2}{3}x+6 \frac{1}{3}$ The points A,B are lying on the line, if and only if the next equality is true: $\displaystyle y=\frac{2}{3}x+6 \frac{1}{3}$ Therefore, $\displaystyle A(x,3) \Rightarrow\\\\3=\frac{2}{3}x+6 \frac{1}{3} \\\\9=2x+19\\\\-10=2x\\\\x=-5$ $\displaystyle B(-2,y)\Rightarrow \\\\y=\frac{-4}{3}+6 \frac{1}{3} \\\\y=5$