Question

Which equation represents the black line?

Which equation represents the red line?
Explain a mathematical way to find the intersection of the lines without actually graphing the lines.

Answer 1

Black Line y = 3 + 2x , y = 2x +3

Red Line y = -2 - .5x. y = -.5x -2

vice versa

Explanation:

For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x

For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.