Plotting Linear Graphs
Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line
What a learner can do afterwards
- Generate a table of (x, y) values for a linear equation and plot the points accurately
- Rearrange an equation such as 2x + 3y = 12 into the form y = mx + c
- Calculate the gradient between two coordinate points using rise over run
1 · Read
A linear equation like y = 2x + 1 has many solutions, but you only need a few to draw its graph. Pick some x-values, work out the matching y-values, then plot each pair as a point.
For y = 2x + 1, build a table. When x = -1, y = 2(-1) + 1 = -1. When x = 0, y = 1. When x = 1, y = 3. When x = 2, y = 5. Plot (-1, -1), (0, 1), (1, 3), (2, 5), then draw a straight line through them.
Some equations are not written as y = mx + c yet. Take 2x + 3y = 12. Subtract 2x from both sides: 3y = 12 - 2x. Divide everything by 3: y = -(2/3)x + 4. Now m = -2/3 and c = 4.
To find a gradient from two points, use rise over run: gradient = (change in y) divided by (change in x). For the points (1, 3) and (4, 9): rise = 9 - 3 = 6, run = 4 - 1 = 3, so gradient = 6/3 = 2.
Always subtract the points in the same order for both x and y. Mixing the order flips the sign of your gradient.
Build a table of values to plot a line, rearrange to y = mx + c to read the gradient and intercept, and find the gradient with rise over run.
The rewritten readings were written for this dataset.
2 · Watch
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.