Equations of lines – WJECy = mx + c

Look at how to plot in all four quadrants of a graph and draw straight lines. We can determine information about the gradient and position of the lines, such as if they are parallel or perpendicular.

Part ofMathsAlgebra

y = mx + c

If we are given equation of the line instead of the graph, we can still determine the gradient.

Equations of straight-line graphs are given in the form:

An equation of straight line y = mx = c where m is the gradient of the line and c is the interceptor of the line on the y axis.

\(\text{y = 2x - 1}\)

The gradient is 2 and the graph will cross the \(\text{y}\)-axis at -1.

\(\text{y = -4x + 5}\)

The gradient is -4 and the graph will cross the \(\text{y}\)-axis at 5.

We can also use this to determine the equation of a straight-line graph.

Example

We need to know the gradient and the \(\text{y}\) to determine the equation of the line.

A graph with a line showing the equation y = 3x + 1.

Gradient = 3 ÷ 1 = 3

\(\text{y}\) intercept = 1

Therefore, the equation of the line is \(\text{y = 3x + 1}\)

Question

What is the equation of this line?

A graph showing the equation y = 2x - 3.

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