Using algebra, find the point at which the line f ( x ) = − 3 x + 2 intersects the line h ( x ) = 4 x + 2

Question

Using algebra, find the point at which the line  intersects the line 

(x,y)=(___,___)

Answer 1

To find the solution to a system of linear equations, which represents the intersection point (if any), we need to set both functions equal to each other:

− 3 x + 2 = 4 x + 2

0 = 7x

x = 0

After solving for the x-coordinate, we need to find the corresponding y-coordinate by substituting into either of the equations:

f(0) = − 3*(0) + 2 = 2

Hence, our solution is (0,2), and you can confirm by substituting this point into both equations to confirm that it is true for both.

Cheers!