---
title: "Plotting Linear Graphs"
description: "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"
canonical: https://lightmysky.com/learn/mathematics/plotting-linear-graphs-mt_-3udyo6VyB
source: https://lightmysky.com/learn/mathematics/plotting-linear-graphs-mt_-3udyo6VyB.md
retrieved: 2026-10-19
---

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# 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

Subject: Mathematics · Area: Algebra · Ages 12 to 14
Page: https://lightmysky.com/learn/mathematics/plotting-linear-graphs-mt_-3udyo6VyB

## Ready when they can

- 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

## Lesson: Plotting Straight-Line Graphs

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.

**Example.** 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.

*(drawing: Each pair from the table becomes one point. Plot them and they line up perfectly, ready for a ruler.)*

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.

**Example.** 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.

**Tip.** Always subtract the points in the same order for both x and y. Mixing the order flips the sign of your gradient.

**Recap.** 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.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU)
- [Linear Function Graphs](https://lightmysky.com/learn/mathematics/linear-function-graphs-mt_WBdHkc2HTf)

## Opens up

- [Forms of the Equation of a Straight Line](https://lightmysky.com/learn/mathematics/forms-of-the-equation-of-a-straight-line-mt_dhIIxdFwcp)
- [Quadratic Graphs](https://lightmysky.com/learn/mathematics/quadratic-graphs-mt_GZuoYaDdWd)
- [Motion Graphs: Gradients and Areas](https://lightmysky.com/learn/mathematics/motion-graphs-gradients-and-areas-mt_KhJeCMYBSL)
- [Simultaneous equations](https://lightmysky.com/learn/mathematics/simultaneous-equations-mt_mqgu72aCMz)
- [Graphical Inequalities and Regions in the Plane](https://lightmysky.com/learn/mathematics/graphical-inequalities-and-regions-in-the-plane-mt_sKerzcAcNy)
- [Reading solutions from a graph](https://lightmysky.com/learn/mathematics/reading-solutions-from-a-graph-mt_Yw27nweoTj)