🐱 Cat + Equations!
Alishba's cat knocks 3 items off the shelf every hour. After 2 hours, 8 items have been knocked off. The equation: if rate = 3 items/hour (slope), and at t=2 there are already 8 items knocked off... y − 8 = 3(x − 2) → y = 3x + 2. That's writing an equation from a slope and a point! 😹
✏️ Worked Example — Read This First!
Write the equation in slope-intercept form for the line through (−3, 1) and (0, −4).
1
Find the slope.
m = (y₂ − y₁) ÷ (x₂ − x₁) = (−4 − 1) ÷ (0 − (−3)) = −5 ÷ 3 = −5/3
m = (y₂ − y₁) ÷ (x₂ − x₁) = (−4 − 1) ÷ (0 − (−3)) = −5 ÷ 3 = −5/3
2
Find the y-intercept (b).
One of our points is (0, −4) — x = 0 means this IS the y-intercept! So b = −4.
One of our points is (0, −4) — x = 0 means this IS the y-intercept! So b = −4.
3
Write the equation.
y = mx + b = −(5/3)x + (−4) = −(5/3)x − 4
y = mx + b = −(5/3)x + (−4) = −(5/3)x − 4
4
Verify using (−3, 1): y = −(5/3)(−3) − 4 = 5 − 4 = 1 ✓
y = −(5/3)x − 4
💡 If neither point has x = 0: find m first, substitute ONE point into y = mx + b, then solve for b.
EasyQuestions 1–3 — slope and y-intercept given
Question 1 EasySee Answer →
Write the equation in slope-intercept form for a line with slope = 3 that passes through the point (0, 2).
Working space
Question 2 EasySee Answer →
Write the equation in slope-intercept form: slope = −2, y-intercept = 5.
Working space
Question 3 EasySee Answer →
Write the equation in slope-intercept form: slope = 1/3, passes through (0, −1).
Working space
MediumQuestions 4–8 — two points and tables
Question 4 MediumSee Answer →
Write the equation in slope-intercept form for the line through (2, 7) and (4, 11).
Working space — find m, then substitute one point to find b
Question 5 MediumSee Answer →
Write the equation in slope-intercept form for the line through (−1, 4) and (3, −4).
Working space
Question 6 MediumSee Answer →
Len is counting how many balloon animals he can make. Write the equation in slope-intercept form.
| x (attempts) | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| y (successful) | 3 | 7 | 11 | 15 |
Working space — find m (rate of change), then find b using the equation
Question 7 MediumSee Answer →
Miku's cat loses weight after its vet puts it on a diet. Write the equation in slope-intercept form.
| x (weeks) | −2 | 0 | 2 | 4 |
|---|---|---|---|---|
| y (weight kg) | 8 | 2 | −4 | −10 |
Working space
Question 8 MediumSee Answer →
Alishba's cat chases a toy. Write the equation in slope-intercept form for the line through (−4, 5) and (2, −4).
Working space — watch out for fraction slope!
HardQuestions 9–10
Question 9 HardSee Answer →
Write the equation in slope-intercept form for the line through (6, 1) and (−3, 7). Show all steps.
Working space
Question 10 HardSee Answer →
Rin records how much icing she puts on cupcakes. Write the equation in slope-intercept form, then use it to predict the y-value when x = 10.
| x | −6 | −2 | 2 | 6 |
|---|---|---|---|---|
| y | −9 | −1 | 7 | 15 |
Working space
🎈 Balloon Animal Tip — Writing Equations from Two Points!
When learning balloon animals, practice is everything. Here's a real pattern: after 5 minutes of practice, a beginner can make 1 animal. After 20 minutes, they can make 4 animals. The slope = (4−1)÷(20−5) = 3÷15 = 1/5 animals per minute. Using the point (5,1): 1 = (1/5)(5) + b → b = 0. So y = (1/5)x. After 60 minutes of practice, that's y = (1/5)(60) = 12 animals per hour — you're getting good! 🎈