Graphing Linear Equations Worksheets

Equation, table, grid

Every problem gives you an equation in the form y = mx + b, a short x/y table to fill in, and a labelled coordinate grid with axes and unit gridlines to plot on.

Four problems by default, laid out two to a row, up to six on a page. The answer key gives two points that lie on each line.

The table is the method

It is printed rather than left to the pupil because the table is the technique, and pupils who skip it plot from intuition and get it wrong.

Pick three x values, substitute each into the equation, get three y values, plot the three points. Three, not two — two points define a line and give you no way of knowing whether you made an arithmetic error, while three that fail to line up tell you immediately that one of them is wrong.

Choose 0 as one of them. Substituting zero is trivial and it lands you on the y-intercept, which is a useful check in itself.

What m and b mean on the page

Worth connecting explicitly, because pupils can plot correctly for months without noticing.

b is where the line crosses the y-axis. Look at y = 2x + 3 and you know before plotting anything that it passes through (0, 3). m is the steepness: from any point, go one right and m up. A negative m goes down instead, which is why those lines slope the other way.

A pupil who has that can sketch a line without a table at all, and can tell at a glance that a plotted line is wrong.

Common errors

Sign errors on negative gradients, by a distance. Then substituting into the wrong variable. Then plotting (y, x) instead of (x, y), which is the coordinate-order error arriving in new clothing.

The three-point rule catches all of them, which is why it is worth insisting on rather than allowing two.

Reading the answer key

It lists two points rather than drawing the line, and that is deliberate: there is no other honest way to give an answer for a graph on paper.

Check the pupil's line passes through both. If it does, the line is right, whatever the pencil work looks like.

Level and next steps

Usually ages twelve to fifteen. It needs coordinates to be secure first, and it leads into simultaneous equations — where two lines crossing is the same thing as the algebraic solution, which is a genuinely satisfying moment for a class that has done both.

See also systems of equations.