On the graph of the function y = -3x + 10 find the intersection point whose coordinate is equal to its abscissa.

In order to find the abscissa point of which is equal to the ordinate, if the function is given by the formula y = -3x + 10, we will compose and solve the following equation.

In other words, we need to solve the equation provided that y = x.

We make a substitution in the equation and solve the resulting linear equation.

x = -3x + 10;

We group the terms with and without variables in different parts of the equation. When transferring terms from one side of the equation to another, we change the sign of the term to the opposite.

x + 3x = 10;

4x = 10;

x = 10: 4;

x = 2.5.

Answer: (2.5; 2.5)