Straight-line graphs and coordinates
Every straight-line graph is an equation in disguise. Read the gradient and the intercept and you have the equation.
Part of your national curriculum
- Algebra: Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions
Lesson overview
What you'll learn in this lesson
Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions
Key learning points
- • Four quadrants
- • y = mx + c
- • Sketching quickly
This lesson at a glance
- 30 minutes
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Visual introductionPicture this
Straight-line graphs and coordinates
Every straight-line graph is an equation in disguise. Read the gradient and the intercept and you have the equation.
In a nutshell
Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · Four quadrants
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
Four quadrants
Coordinates are always (x, y): across first, then up or down. Negative x is left of the origin, negative y is below it.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 17
Learn
y = mx + c
m is the gradient — how far up for each one across. c is where the line crosses the y-axis. y = 2x + 1 climbs two for every one, starting at 1.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 17
Learning cycle 2 of 2
Part 2 · Sketching quickly
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Sketching quickly
Plot the intercept, then step out the gradient once and join the points. Check with a third point; if it is off the line, one of your calculations is wrong.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 17
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 14 of 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ are always (x, y): across first, then up or down.
Challenge round
Part 15 of 17
Game · Recall cards
Which point lies in quadrant III?
Card 1 of 4
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Straight-line graphs and coordinates
4 questions, marked with the reasoning shown. No timer.
1. Which point lies in quadrant III?
2. For y=2x+1, find y when x=3.
3. What is the gradient of y=−3x+4?
4. What is the gradient of y = 3x − 4?
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 17 · Watch & discover
How this is going
- Not looked at yet
Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions