Line Through Two Points and Slope
Graph and Slope of a straight line
The graph of a function of the form is a line.
This is why all the functions of this form are called linear functions.
If we know the coordinates of two points of the line, and , we can calculate the slope of the line: .
The slope is a constant value: however you choose two points on the line, the value of m is always the same.
Try it yourself...
In the app below, move points and , then determine the value of the slope of your line .
Select CHECK to get a feedback for your answer and view the solution of this exercise.
When things go wrong algebraically...
If you have the equation of a line and / or the coordinates of two of its points, and , you can calculate:
- the value of the y-intercept
- the value of the slope, using the formula .
Move points A and B in the app above, and align them vertically.
You will discover which is the algebraic issue that is generated by such a configuration.
... and geometrically
Move points A and B in the app above, and align them vertically. Observe the graph of the line. Is this the graph of a linear function? Explain your conjectures.