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
The lesson
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.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.