Learn how two numbers, the gradient and the intercept, describe any straight line.
Lesson 1 of 6 in Mathematics
A taxi charges £2 to start, then £3 for every kilometre. If is the distance and is the cost, then
Plot this on a graph and you get a perfectly straight line. Equations like this are called linear equations, because their graphs are lines. Every straight line can be described with just two numbers. Learn to read them, and you can picture a graph without drawing it.
Every straight line (except vertical ones) can be written as
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That was a free sample. The rest is for schools on RudimentaryLabs.
Next up: Introducing simultaneous equations, one of 5 more lessons in Mathematics.
Make a table for :
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| 1 | 3 | 5 | 7 |
Each time goes up by 1, goes up by 2. That is the gradient. And when , . That is the intercept.
Finding the gradient from two points. Pick two points on the line and use
A negative gradient means the line slopes down from left to right. For example, falls by 3 for every step right.
A line passes through the points and . Find its equation.
Step 1. Find the change in (the rise).
Step 2. Find the change in (the run).
Step 3. Divide to get the gradient.
Step 4. Find the intercept. The line passes through , so it crosses the -axis at . That means .
Step 5. Put it together: .
Check with the other point: when , . ✓
Straight-line graphs model anything with a fixed starting amount and a steady rate: phone bills, taxi fares, a candle burning down, or water filling a tank. Scientists draw lines of best fit through data and use the gradient to measure rates, such as speed from a distance–time graph.
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