Find the coordinates of the intersection points of the graphs of the function y = -2x + 8 and y = 0.5x + 3

In order to find the coordinates of the intersection point of the graphs of the function y = -2x + 8 and y = 0.5x + 3, we will compose and solve a system of these equations.

System of equations:

y = -2x + 8;

y = 0.5x + 3.

We will solve the system by the substitution method.

We substitute in the first equation instead of y the expression from the second equation.

System of equations:

0.5x + 3 = -2x + 8;

y = 0.5x + 3.

We solve the first equation of the system:

0.5x + 2x = 8 – 3;

2.5x = 5;

x = 5: (2.5);

x = 2.

System of equations:

x = 2;

y = 0.5 * 2 + 3 = 1 + 3 = 4.

Answer: intersection point (2; 4).