Simple Math Question??

Question

I've never understood graphs and such

A line contains the points (1,4) and (6, -21).

Find teh value of (a) such that the point (2, a) lies on the line

I know the equation mx+b. I know the slope is -5. How do I figure out the question above? (without graphing)

Answer 1

So first, you want to find the equation of the line that goes through the points (1,4) and (6,-21)

So, m = (4 - (-21))/(1 - 6) = 25/-5 = -5

So y = -5x + b

We use one of the points to find the y-intercept b (Take (1,4))

4 = -5(1) + b

Therefore, b = 9, and the equation of the line is

y = -5x + 9

Now that you have the equation, since (2, a) passes through the line, it must satisfy the equations. You plug in x = 2 to find a. Note that 'a' is just the y value when x = 2.

y = -5(2) + 9

y = -1

Therefore a = -1

Answer 2

the change in x is one so the change in y is -5 so (2,-1)