Linear functions and slope – Grade 9 math lesson
Lesson 14 of 17 in the Grade 9 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 9 (ages 14–15) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 9 (ages 14–15)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
Learning goal: find slopes and equations of lines (y = mx + b).
Success looks like
- I can find a gradient.
- I can write the equation of a line.
- I can recognize parallel and perpendicular lines.
Key words
- slope
- 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 line has the equation y = mx + b. The slope m is the steepness; b is the y-intercept, where the line crosses the y-axis.
Slope = change in y ÷ change in x between two points on the line.
Parallel lines have the same slope. Perpendicular slopes multiply to −1.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 9 math lessons
- Rates and unit rates
- Converting units
- Upper and lower bounds
- Simplifying expressions
- Expanding expressions
- Factoring
- Solving equations
- Inequalities
- Rearranging formulas
- Systems of equations
- Quadratic equations
- Identities and proof
- Arithmetic and geometric sequences
- Functions
- Graphing functions
- Exponential functions
Curriculum
Common Core State Standards HSA.REI.D.10: “Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).”
Common Core State Standards 8.F.B.4: “Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.