Question

A line passes through the points (-3, -2)and (2,1). Does it also passed through the points (5,3)

Answer 1

Hi!

Let's write it in slope intercept form first.

y = mx + b

Subtract y intercepts
1 - (-2) = 3

Subtract x intercepts
2 - (-3) = 5

y = 3/5x + b

Substitute one of the points to find y intercept.
1 = 3/5 · 2 + b
1 = 1.2 + b
-0.2 = b

y = 3/5x - 0.2

Now substitute the point (5,3), and if the equation is still correct, then it does pass through that point.

5 = 3/5 · 3 - 0.2
5 = 1.8 - 0.2
5 = 1.6

Since the equation is in correct, the line does NOT pass through the point (5,3).

Hope this helps! :)