The graph of a function of the form [math]y=mx+b[/math] is a [i]line[/i]. [br]This is why all the functions of this type are named [i]linear functions[/i].[br][br]If we know the coordinates of two points of the function, [math]P_1=\left(x_1,y_1\right)[/math] and [math]P_2=\left(x_2,y_2\right)[/math], we can calculate the [i]slope[/i] [math]m[/math] of the line: [math]m=\frac{y_2-y_1}{x_2-x_1}[/math]. This is a constant value: however you choose two points on the line, the value of [i]m[/i] is always the same.

In the app below, move points [math]A[/math] and [math]B[/math], then enter in the input box the value of the slope [math]m[/math] of the line that you have defined.[br]Select [i]Check answer[/i] to get a feedback for your answer and view the solution of this exercise.[br]Deselect [i]Check answer[/i] to create a new line and calculate its slope.

If you have the equation of a linear function [math]f\left(x\right)=mx+b[/math] and the coordinates of two of its points, [math]P_1=\left(x_1,y_1\right)[/math] and [math]P_2=\left(x_2,y_2\right)[/math], you can calculate: [br]- the value [math]b[/math] of the [i]y[/i]-intercept[br]- the value [math]m[/math] of the slope, using the formula [math]m=\frac{y_2-y_1}{x_2-x_1}[/math].[br][br]Move points [i]A[/i] and [i]B[/i] in the app above, and align them vertically.[br]You will discover which is the algebraic issue that is generated by such a configuration.