The function is given by the formula y = 42x-84, without performing constructions, determine the coordinates

The function is given by the formula y = 42x-84, without performing constructions, determine the coordinates of the intersection points of this function: a) with the coordinate axes b) with the function y = -42x + 84

Solution:

a) Find the coordinates of the point of intersection of the graph of the function y = 42 x – 84 with the Ox axis. In this case, y = 0. We obtain and solve the equation:

42 x – 84 = 0,

42 x = 84,

x = 84: 42,

x = 2.

The point of intersection of the graph of the function y = 42 x – 84 with the Ox axis has coordinates (2; 0).

Let’s find the coordinates of the point of intersection of the graph of the function y = 42 x – 84 with the Oy axis. In this case, x = 0. We get:

y = 42 * 0 – 84 = – 84.

The point of intersection of the graph of the function y = 42 x – 84 with the Oy axis has coordinates (0; – 84).

b) To determine the coordinates of the intersection points of two functions without constructing, it is necessary to equate their right-hand sides and solve a linear equation with one variable.

42 x – 84 = – 42 x + 84,

42 x + 42 x = 84 + 84,

84 x = 168,

x = 168: 84,

x = 2.

Answer: a) (2; 0); (0; – 84); b) x = 2.