๐ต Len Kagamine Fun Fact!
Kagamine Len's voice is synthesised at a sample rate of 44,100 Hz โ meaning 44,100 data points per second of audio. If you plotted time (x) against the number of data points processed (y), the slope would be 44,100. That's one steep line! ๐
โ๏ธ Worked Example โ Read This First!
Find the slope of the line that passes through the points (2, 1) and (6, 9).
Full Solution (show working like this in every question)
1
Label the points.
(xโ, yโ) = (2, 1) (xโ, yโ) = (6, 9)
2
Write the slope formula.
m = (yโ โ yโ) รท (xโ โ xโ)
3
Substitute the values.
m = (9 โ 1) รท (6 โ 2) = 8 รท 4
5
State the answer with units if applicable.
m = 2
โ ๏ธ Always subtract in the same order: (yโ โ yโ) over (xโ โ xโ). Mixing the order is the most common mistake!
Find the slope of the line shown in the graph below.
Working space
Find the slope of the line shown in the graph below.
Working space
Find the slope of the line shown in the graph below.
Working space
Find the slope of the line shown in the graph below.
Working space
Find the slope of the line that passes through the points (1, 4) and (5, 12).
Working space โ label your points, write the formula, substitute, simplify
Find the slope of the line that passes through the points (โ2, 7) and (4, โ5).
Working space
Miku is recording a new song. The table below shows the number of minutes elapsed (x) and the number of bars she has recorded (y). Find the rate of change and state what it means.
| x (minutes) | 0 | 2 | 4 | 6 |
|---|
| y (bars) | 1 | 7 | 13 | 19 |
|---|
Working space โ calculate ฮy รท ฮx using any two rows
Find the slope of the line that passes through the points (3, 1) and (6, 3). Express your answer as a fraction in lowest terms.
Working space
Len is practising balloon animals. The table below shows the number of hours he has practised (x) and the number of balloon animals he can make in one hour (y).
| x (hours practised) | 1 | 3 | 5 | 7 |
|---|
| y (animals per hour) | 8 | 24 | 40 | 56 |
|---|
a) Calculate the rate of change.
b) What does the rate of change mean in the context of this problem?
Working space
Find the slope of the line that passes through the points (โ2, 1/2) and (4, 7/2). Show all steps carefully.
Working space โ be careful with the fraction arithmetic
๐ Balloon Animal Tip โ The Poodle Basic Shape
To make a basic balloon poodle, start with a long balloon (260Q). Inflate it leaving about 3 inches uninflated at the end. Make a 2-inch bubble, then twist it twice to lock. Make three more 2-inch bubbles, then fold and twist the 3rd and 1st together to make an ear loop! The maths: if each bubble is 2 inches and your balloon is 60 inches long, you can make at most 30 bubbles โ that's enough for a full poodle dog with legs, ears, neck and tail! ๐ฉ