🎵 Len Fact — Slope in Music!
In Len Kagamine's song "Servant of Evil", the tempo is 160 BPM (beats per minute). If you wrote an equation for the total beats B after t minutes: B = 160t. That's slope-intercept form with m = 160 and b = 0! The slope tells you how fast the song moves. 🎶
✏️ Worked Example — Read This First!
For the equation y = −2x + 5:
a) Identify the slope and y-intercept.
b) Describe what the slope tells you about the graph.
a) Identify the slope and y-intercept.
b) Describe what the slope tells you about the graph.
Full Solution
1
Compare to y = mx + b.
y = −2x + 5 → m = −2 b = 5
y = −2x + 5 → m = −2 b = 5
2
Interpret m = −2: The line goes down 2 units for every 1 unit it moves right (negative slope = falling line).
3
Interpret b = 5: The line crosses the y-axis at the point (0, 5).
Slope m = −2 | y-intercept b = 5 | y-intercept point: (0, 5)
⚠️ The y-intercept is always the point (0, b) — always include the zero for the x-coordinate when asked to write it as a coordinate pair!
EasyQuestions 1–3 — Identify m and b
Question 1 EasySee Answer →
For the equation y = 3x − 7, identify the slope (m) and the y-intercept (b). Write the y-intercept as a coordinate pair.
Working space
Question 2 EasySee Answer →
For the equation y = −(1/2)x + 4, identify the slope (m) and the y-intercept (b). Then describe whether the line rises or falls from left to right.
Working space
Question 3 EasySee Answer →
For the equation y = x − 1, identify the slope (m) and the y-intercept (b). (Hint: what is the coefficient of x when there is no number written?)
Working space
MediumQuestions 4–8
Question 4 MediumSee Answer →
Write the equation in slope-intercept form for a line with slope m = 4 and y-intercept b = −3.
Working space
Question 5 MediumSee Answer →
Write the equation in slope-intercept form for a line with slope m = −3/4 and y-intercept b = 2.
Working space
Question 6 MediumSee Answer →
Write the equation in slope-intercept form for the line shown in Graph A below. (Identify the y-intercept and use two points to find the slope.)
Graph A — Q6
Working space — write slope calculation, then the equation
Question 7 MediumSee Answer →
Write the equation in slope-intercept form for the line shown in Graph B below.
Graph B — Q7
Working space
Question 8 MediumSee Answer →
Rin is baking macarons. The table below shows the number of trays she has baked (x) and the total number of macarons (y). Write the equation in slope-intercept form.
| x (trays) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y (macarons) | 5 | 8 | 11 | 14 |
Working space — find m from the rate of change, find b from the table where x=0
HardQuestions 9–10
Question 9 HardSee Answer →
Miku is practising a new song. The table shows time in minutes (x) and remaining pages of sheet music (y). Write the equation in slope-intercept form.
| x (minutes) | −3 | 0 | 3 | 6 |
|---|---|---|---|---|
| y (pages left) | 10 | 4 | −2 | −8 |
Working space — find rate of change first, then use where x=0 to find b
Question 10 HardSee Answer →
Write the equation in slope-intercept form for the linear function given by this table.
| x | −4 | −1 | 2 | 5 |
|---|---|---|---|---|
| y | 15 | 9 | 3 | −3 |
Working space — find m, find b by substituting a known point
🧁 Baking Maths Tip!
When scaling a cake recipe, linear equations are your best friend! If a recipe uses 200g of flour for 12 cupcakes (and 0g for 0 cupcakes), the equation is y = (200/12)x ≈ 16.7x — the slope is the grams of flour per cupcake. Want to make 30 cupcakes? y = 16.7 × 30 = 500g. That's slope-intercept form in action right in your kitchen! 🍰