Straight lines, curves and sequences
A graph turns an equation into a picture. Reading gradient, intercepts and shape lets you answer questions that would be laborious algebraically.
Lesson overview
What you'll learn in this lesson
Manipulate algebraic expressions, solve equations and interpret graphs of functions.
Key learning points
- • Straight-line graphs
- • Recognising curves
- • Sequences
This lesson at a glance
- 30 minutes
- 19 parts to scroll through
- 4 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 19
Visual introductionPicture this
Straight lines, curves and sequences
A graph turns an equation into a picture. Reading gradient, intercepts and shape lets you answer questions that would be laborious algebraically.
In a nutshell
Manipulate algebraic expressions, solve equations and interpret graphs of functions.
Learning cycle
Part 2 of 19
Learning cycle 1 of 2
Part 1 · Straight-line graphs
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 19
Learn
Straight-line graphs
In y = mx + c, m is the gradient and c the y-intercept. Gradient is the change in y divided by the change in x between two points. Parallel lines share a gradient; perpendicular gradients multiply to −1, so a line perpendicular to y = 2x + 1 has gradient −½.
Reset break
Part 4 of 19
Pause
That's sitting 1 of 5 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 19
Learn
Recognising curves
A quadratic gives a parabola, positive coefficient opening upwards. A cubic has a characteristic double bend, a reciprocal graph two separate branches with asymptotes, and an exponential rises ever more steeply while never reaching zero. Sketch questions reward the correct shape and intercepts, not perfect plotting.
Quick check
Part 6 of 19
Quick check
Part 7 of 19
Reset break
Part 8 of 19
Pause
That's sitting 2 of 5 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 19
Learning cycle 2 of 2
Part 2 · Sequences
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 19
Learn
Sequences
For a linear sequence the nth term is (common difference)n plus an adjustment: 5, 8, 11, 14 has difference 3, and 3n gives 3, 6, 9, so the nth term is 3n + 2. For quadratic sequences, a constant second difference of 2a identifies the n² coefficient. Always check your rule on the first and a later term.
Quick check
Part 11 of 19
Reset break
Part 12 of 19
Pause
That's sitting 3 of 5 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.
Quick check
Part 13 of 19
Explore the idea
Part 14 of 19
Worked example
Worked answer: find the equation of the line through (1, 5) and (4, 14) (3 marks)
Gradient m = (14 − 5) ÷ (4 − 1) = 9 ÷ 3 = 3 (1). Substituting the point (1, 5) into y = 3x + c gives 5 = 3 + c, so c = 2 (1). The equation is y = 3x + 2 (1). Verifying with the second point: 3(4) + 2 = 14, correct. Subtracting the coordinates in inconsistent order is the usual error.
Challenge round
Part 15 of 19
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
Reset break
Part 16 of 19
Pause
That's sitting 4 of 5 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 17 of 19
Game · Recall cards
The gradient of a line perpendicular to y = 4x − 1 is
Card 1 of 4
Mastery quiz
Part 18 of 19
Marked quiz
End of lesson quiz: Straight lines, curves and sequences
4 questions, marked with the reasoning shown. No timer.
1. The gradient of a line perpendicular to y = 4x − 1 is
2. The nth term of 5, 8, 11, 14 is
3. A graph with two separate branches and asymptotes is
4. A quadratic sequence is identified by a constant
Lesson round-up
Part 19 of 19
Lesson round-up
Ready when you are
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Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 19 · Watch & discover