Find the coordinates of the point of intersection of the graphs of linear functions

Find the coordinates of the point of intersection of the graphs of linear functions and draw a coordinate straight line: y = 3x + 2 and y = -0.5x-5.

1. Finding the intersection point y = 3x + 2 and y = -0.5x – 5. Looking for the x coordinate:

3x + 2 = -0.5x – 5;

3x + 0.5x = -5 – 2;

3.5x = – 7;

x = -7 / 3.5;

x = -2.

We calculate the coordinate y:

y = 3 * (-2) + 2 = -6 + 2 = -4.

Answer: The point of intersection is y = 3x + 2 and y = -0.5x – 5: (-2; -4).

2. We build graphs y = 3x + 2 and y = -0.5x – 5. For this we need two points for each line:

a) For x = 0, y = 3 * 0 + 2 = 2;

at x = 2, y = 3 * 2 + 2 = 6 + 2 = 8.

b) When x = 2, y = -0.5 * 2 – 5 = -6;

at x = 0, y = -0.5 * 0 – 5 = -5.