Question

Find the value of r so that the line passes through (9,13) and (5,r) has a slope of m=1/2.

Answer 1

r=11. This is because you can use the point slope formula. y = mx + b. Plug 9 in for x and 13 in for y. The slope of 1/2 is m. You will then find b which is the y-intercept. Then rewrite the equation as y=1/2x+8.5. Plug 5 in for x and then simplify the equation. You will discover that y, which is r, is 11.

Answer 2

Definition of slope between two points

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

With the values we know plugged in

`\frac{1}2=(r-13)/(5-9)`

5-9 evaluates to -4.

`\frac{1}2=(r-13)/(-4)`

We could do a number of things from here to solve this.
- Since the bottom multiplies by -2 from the first fraction to the next, so does the top...1 × -2 = -2. Therefore, r-13 = -2. Add 13 to each side to get r = 11.
- Multiply each side by -4. -2 = r-13...see above
- Cross multiply to get 1(-4) = 2(r-13) ⇒ -4 = 2r - 26 ⇒ 22 = 2r ⇒ r = 11


`\boxed{r=11}`