Straight-line graphs – Year 10 maths lesson

Lesson 28 of 37 in the Year 10 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 10 (ages 14–15) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.

Time: 45 minutes + 20 min homework
Year: Year 10 (ages 14–15)
You need: Paper, a pencil and this page
Marked: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “What do the m and the c tell you about a line?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Calculating change in x ÷ change in y. Rise over run: change up ÷ change across.
Missing the minus sign for a line going down. Going down from left to right means a negative gradient.

Tip for home: Look at taxi fares or phone plans: a fixed charge plus a cost per unit is a straight line.

What your child will learn

We are learning to find gradients and equations of straight lines (y = mx + c).

Success looks like

I can find a gradient.
I can write the equation of a line.
I can recognise parallel and perpendicular lines.

Key words

gradient: the steepness of a line
y-intercept: where the line crosses the y-axis
parallel: same steepness, never meeting
perpendicular: meeting at a right angle

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Plot y = 2x + 1 from a table of values, then change the 2 and the 1 to see what happens.

The big ideas (for the adult)

A straight line has the equation y = mx + c. The gradient m is the steepness; c is where the line crosses the y-axis.

Gradient = change in y ÷ change in x between two points on the line.

Parallel lines have the same gradient. Perpendicular gradients multiply to −1.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Marked by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, marked by Classfern
Independent practice	15 min	Marked by Classfern
Plenary and exit ticket	6 min	Marked by Classfern, self-checked

Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.

More practice

All Year 10 maths lessons and tests · Maths Department

Curriculum

National Curriculum for England, Year 10: “use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through 2 given points, or through 1 point with a given gradient”

National Curriculum for England, Year 10: “translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or 2 simultaneous equations), solve the equation(s) and interpret the solution”

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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.