Determine the point on the graph of the linear function y = 5x − 3, the abscissa of which is equal to the ordinate.

In order to determine the point of the graph of the linear function y = 5x – 3, the abscissa of which is equal to the ordinate, that is, x = y, we must solve the linear equation with one variable.

x = 5x – 3;

We solve the equation using identical transformations.

We transfer the terms with variables to the left side of the equation. When transferring terms from one side of the equation to another, we change the sign to the opposite:

x – 5x = -3;

x (1 – 5) = -3;

-4x = -3;

We are looking for an unknown factor:

x = -3: (-4);

x = 3/4;

x = 0.75.

Answer: x = 0.75.