The equation of a linear graph is y=mx+c. Given values of m and c, this equation can be used to plot a straight line graph.
Reminder of y=mx+c
The gradient of a line is given by m. It indicates the steepness of the line and can be calculated with:
m=change in xchange in y
The y-intercept is given by c. This is the point on the y-axis where the line crosses.
Using y=mx+c to draw the line
One way to draw a straight line graph is to figure out two points that the line passes, before joining up those points and extending the line beyond them. Follow this procedure:
PROCEDURE
1.
The easiest point to start with is the y-intercept, given by c, since you know this is on the y-axis. Hence you have that the point (0,c) is on the line. Mark this on the coordinate grid.
2.
To find another point, simply pick an x-value (other than zero, since this will just give you the point you already have) and insert it into the equation of the line to find the corresponding y-coordinate.
3.
Mark on this second point and join it up with the first point.
Example
A line has equation y=3x−4. Find the coordinates of two points on the line. Hence draw the line given by the equation.
Firstly, use the y-intercept (x=0) to find the first point: c=−4
Point 1: (0,−4)
Next, pick a non-zero x-value. In this instance,x=1. Insert this into the equation of the line:
y=3x−4=3(1)−4=3−4=−1
Point 2: (1,−1)
Plot the two points found ((0,−4) and (1,−1)) then join them up, extending beyond those points.
Exceptions
Not all linear graphs have the equation y=mx+c. Vertical lines have equations of the formx=d whered is a constant. These lines have the samex-coordinate all along the line, so are represented by a vertical line going throughx=d given a value ofd.
Horizontal lines technically do have the formy=mx+c but wherem=0. These are just horizontal lines that go throughc on they-axis.
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Straight line graphs
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Drawing straight line graphs
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FAQs - Frequently Asked Questions
What shape is a linear graph?
A linear graph is a straight line.
What is a linear equation?
y=mx+c is a form of the linear equation. It gives a straight line when plotted.
How do you use an equation of a line to find a point on the line?
Choose any x-coordinate and insert it into the equation of the line. This will give the y-coordinate. Hence you have the coordinates of a point on the line.
How do you plot a linear graph from the equation?
Use the equation to locate two points on the line. Join these points up and extend the line beyond them.
