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A Couple of Points on Straight Line Graphs...

Here we look at a great way to construct/sketch a straight line graph that requires just two points.

The two-point gradient and y-intercept method

The equation for a straight line is

Where x and y are variables that relate to the x and y axes of a graph.

The gradient (slope) of the line is given by m - this is the number immediately before the x (it's known as the coefficient). If the coefficient is a negative value, the gradient will slope downwards on a graph.

The c term is the y-intercept - the point on the y-axis where the line will cross.

Look at the following equation...

If it can be manipulated so that it has the form y = mx + c, it can be graphed.

In this case, the line will have a gradient of 3 and will cross the y-axis at y = 4.

The line can be graphed quickly by plotting just two points.

The easiest point to plot is the y-intercept. This occurs when x = 0 so the coordinates will be (0, 4)

The y-intercept

Another point on the graph is needed and it can be found using the value for the gradient, 3.

The gradient is usually found by calculating...