Point-Slope Form

Point-slope form is a way to write the equation of a line when we know two things: the slope and one point on the line.

Imagine a researcher testing a spring by applying different forces and measuring how far it stretches.

Each measurement becomes a data point on a graph, with force on the x-axis and the spring’s stretch on the y-axis. The data points form a straight line, showing that the stretch increases at a constant rate as more force is applied.

By comparing data points on the graph, the researcher calculates the rate of change by dividing the change in stretch by the change in force. This rate of change is called the slope.

Next, the researcher chooses one data point on the graph: (2, 0.08). This means that when the applied force is 2 newtons, the spring stretches 0.08 meters.

Together, the slope and the point give the researcher everything needed to write the equation in point-slope form.

This equation shows how the spring’s stretch depends on the applied force. For example, substituting an applied force of 5 newtons into the equation gives a stretch of 0.2 meters.