Question

Find r if (r, 6) and (5, -4) are two points on a line with a slope of 5/7 (Hint: use the slope formula)

Answer 1

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have

`(r,\ 6),\ (5,\ -4)\\\\m=(5)/(7)`

Substitute

`(-4-6)/(5-r)=(5)/(7)\\\\(-10)/(5-r)=(5)/(7)\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}`