Question

A line passes through point (-2, 5) and has a slope of 2/3. Points A(x, 3) and B(-2, y) lie on the line. The value of x is____, and the value of y is _____.

Please help I've seen this problem on this website before but no one actually answered I know it's probably very simple to get the answer but I don't know how could someone tell me how to or answer it please thanks?

Answer 1

Use the equation y = mx +c
y = 2/3x +c Substitute the slope (m) in
5 = 2/3(-2) +c Substitute the point (-2,5)
5 = -4/3 +c Make C the subject
c = 19/3

y = 2/3x + 19/3 This is the equation of the line.

Next you start subbing the points A and B in separately, using the same equation.

Subbing A(x, 3)
3 = 2/3x + 19/3 Make x the subject to find it.
-10/3 = 2/3x
-5 = x

The point A is (-5,3)

Subbing B(-2, y)
y = 2/3(-2) + 19/3 y is already the subject and you just solve it
= -4/3 + 19/3
y = 5

The point B is (-2, 5)

I hope this helped you, I have also attached a photo of the written work! I'm also sorry if the answer isn't correct... >-<