Construct a graph of the function y = kx + 1, if a point M (1; 3) is given.

Before plotting the graph of the function, which is given by the equation y = kx + 1, if a point M with coordinates (1; 3) is given, through which the graph of this function passes, we will substitute x = 1 into the equation; y = 3 and solve the resulting equation for the variable k:

3 = 1 * k + 1;

k + 1 = 3;

k = 3 – 1;

k = 2.

Let’s write the equation of the straight line:

y = 2x + 1;

In order to build a graph, you need to know the coordinates of two points. One is given to us in the condition, and the coordinates of the second we will calculate:

Let x = 0;

y = 2 * 0 + 1 = 0 + 1 = 1.

(0; 1).