Question

Given the slope of a line, and coordinates for two points on the line, find the unknown value.

Slope: 3
Points: (10,9) and (a,b)

I cannot figure out how to find both of the values, pleas help!

Answer 1

It just so happened that I found the answer this way, but I'm not sure if this is how you should solve this problem.

So I tried to find the slope intercept form, which is y = mx + b.

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

Since you know the slope is 3, you can plug it in.

y = mx + b -----> y = 3x + b

To find "b", you plug in the point you know, which is (10,9) into the equation

y = 3x + b

9 = 3(10) + b

9 = 30 + b

-21 = b

Your equation is y = 3x - 21.

Next I used the slope formula and plugged in what I know:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`3=(b-9)/(a-10)`

Since you are missing a point, I used a point that we found, which was the y-intercept: (0, -21), and plugged it into the equation.

`3=(-21-9)/(0-10)`

`3=(-30)/(-10)`

3 = 3

Your point (a,b) is (0, -21)

a = 0

b = -21