Gradient Intercept Form of a Straight Line: y=mx+c

The most transparent and useful form a straight line is known as the gradient-intercept equation:

y=mx+c

where m is the gradient (or slope of the line) and c is the intercept with the y-axis. The gradient m and c are constants,unlike x and y which are variables; how does this work? The m and c values are fixed to some values, for example m=2 and c=-3 defines the straight line

y=2x-3

x and y are variables which in practice means we pick a value of x and then calculate the value of y ( y is a function of x since it's value depends on x). This process is shown below, where a random x value is selected and is put through a function to calculate the y-value, the coordinate (x,y) is then plotted on the graph. The process is repeated many times; and eventually if you wait long enough you will see that the points have merged to form a line

Example: Plot line given y=mx+c

You are given an equation and you need to plot the line on paper:

Exercise: Draw lines with the same y-intercept c

You are required to plot the line. Move two points so that they are on the line, and then press "line" to draw a line through these points.The lines that are required to draw will all have the same c value but random m values. Repeat the exercise many times, what do you notice?

Exercise: Draw lines with the same m value

Mark two points on the graph then draw the required straight line; repeat the exercise many times. Enter integers between 10 and -10 and press LINE. Press NEXT for next line with same m. Press RESET to start again.

Summary

(i) Drawing a line given an equation is simple: you find two points on the line by picking x-values and calculating the y-values using the equation of the line. A straight line is then draw through two or more points. (ii) The c-value determines the intercept with y-axis, so changing c for fixed m translates the line in the vertical direction, i.e. up or down. (iii) The m value determines the gradient, so changing m for fixed c rotates the line around the y-intercept coordinate. You can investigate this with the sliders below: