SOLUTION: A(-1,2), B (3,a) and C (-3,7) are collinear. Find a

Question 976427: A(-1,2), B (3,a) and C (-3,7) are collinear. Find a
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's find the equation of the line through the two points (-1,2) and (-3,7)

To do that, we use the slope formula to find the slope m.

Note:

is the first point

. So this means that and .
Also,

is the second point

. So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Add 2 to both sides.

Combine like terms.

So the equation that goes through the points

and

is

------------------------------------------------------------------------

Now plug in x = 3 to find y

So the point (3,-8) lies on the same line. Therefore, a = -8
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