Find the coordinates of the intersection point of the graphs of the linear function y = x + 4 and y = 2x.

To find the coordinates of the point of intersection of the graphs of the linear function given by the equations y = x + 4 and y = 2x, we solve the system of equations.

y = x + 4;

y = 2x.

We will solve the system using the substitution method. Let us substitute in the first equation the system instead of y the expression 2x and solve the resulting linear equation with one variable.

2x = x + 4;

y = 2x.

System:

2x – x = 4;

y = 2x.

System:

x = 4;

y = 2x.

Substitute the found value of x into the second equation and find the value of y.

System:

x = 4;

y = 2 * 4 = 8.

Answer: the point of intersection of the lines has coordinates (4; 8).