Question

Write an equation for the line passing through the points (-5,15) and (20,25). Show how you found your answer.

Answer 1

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-5, 15) and (20, 25). substitute:

$m=\dfrac{25-15}{20-(-5)}=\dfrac{10}{25}=\dfrac{2}{5}\\\\y-15=\dfrac{2}{5}(x-(-5))\\\\y-15=\dfrac{2}{5}(x+5)\qquad|\text{use distributive property}\\\\y-15=\dfrac{2}{5}x+2\qquad|\text{add 15 from both sides}\\\\y=\dfrac{2}{5}x+17\qquad|\text{multiply both sides by 5}\\\\5y=2x+85\qquad|\text{subtract 2x from both sides}\\\\-2x+5y=85\qquad|\text{change the signs}\\\\2x-5y=-85$

Answer:

point-slope form: $y-15=\dfrac{2}{5}(x+5)$

slope-intercept form: $y=\dfrac{2}{5}x+17$

standard form: $2x-5y=-85$