⚠️ Top Mistakes on This Topic
- Forgetting the negative sign: y = −2x + 3 has m = −2, NOT m = 2. Always include the sign.
- Writing just the number for y-intercept: If asked for the y-intercept as a point, write (0, b) — not just b.
- Coefficient of 1: In y = x + 5, the slope is 1, not 0. There is an invisible "1" in front of x.
- From a table — forgetting to check b: b is the y-value when x = 0. If x = 0 isn't in the table, you must substitute into the equation after finding m.
Question 1 Easy
y = 3x − 7: identify slope and y-intercept
1
Compare to y = mx + b: m = 3, b = −7
2
y-intercept as a point: (0, −7)
m = 3 | b = −7 | y-int: (0, −7)
Question 2 Easy
y = −(1/2)x + 4
1
m = −1/2, b = 4, y-int: (0, 4)
2
m is negative → the line falls from left to right.
m = −1/2 | b = 4 | Line falls (goes downward)
Question 3 Easy
y = x − 1
1
y = 1x + (−1) → m = 1, b = −1
2
y-int: (0, −1)
m = 1 | b = −1 | y-int: (0, −1)
Question 4 Medium
Write equation: m = 4, b = −3
1
Substitute m and b into y = mx + b: y = 4x + (−3)
y = 4x − 3
Question 5 Medium
Write equation: m = −3/4, b = 2
1
y = (−3/4)x + 2
y = −(3/4)x + 2
Question 6 Medium
Equation from Graph A (line through (0, 1) and (2, 5))
1
y-intercept: line crosses y-axis at 1 → b = 1
2
Pick another point on the line: (2, 5)
3
Slope: m = (5−1)÷(2−0) = 4÷2 = 2
4
Equation: y = 2x + 1
y = 2x + 1
Question 7 Medium
Equation from Graph B (line through (0, −1) and (2, −5))
1
y-intercept: line crosses y-axis at −1 → b = −1
2
Second point on line: (2, −5)
3
Slope: m = (−5−(−1))÷(2−0) = −4÷2 = −2
4
Equation: y = −2x + (−1) = −2x − 1
y = −2x − 1
Question 8 Medium
Rin's macaron table (x=trays, y=macarons): x: 0,1,2,3 / y: 5,8,11,14
1
Rate of change (slope): (8−5)÷(1−0) = 3 → m = 3
2
When x = 0, y = 5 → b = 5
3
Meaning: Rin starts with 5 macarons and adds 3 per tray baked.
y = 3x + 5
Question 9 Hard
Miku's table: x: −3,0,3,6 / y: 10,4,−2,−8
1
Rate of change: (4−10)÷(0−(−3)) = −6÷3 = −2 → m = −2
2
When x = 0, y = 4 → b = 4
3
Verify: x=3 → y = −2(3)+4 = −2 ✓ x=6 → y = −2(6)+4 = −8 ✓
y = −2x + 4
Question 10 Hard
Table: x: −4,−1,2,5 / y: 15,9,3,−3
1
Slope: (9−15)÷(−1−(−4)) = −6÷3 = −2 → m = −2
2
x = 0 is NOT in table — use a point to find b. Use (−1, 9):
9 = −2(−1) + b → 9 = 2 + b → b = 7
9 = −2(−1) + b → 9 = 2 + b → b = 7
3
Verify: x=2 → y = −2(2)+7 = 3 ✓ x=5 → y = −2(5)+7 = −3 ✓
y = −2x + 7
🤖 Stuck? AI Prompts for Topic 2
If you're unsure what m and b are:"Explain slope-intercept form y = mx + b in simple terms for a 9th grader. What does m tell you about the shape of the line? What does b tell you about where it starts?"
If you struggle reading equations from a graph:"How do I find the equation y = mx + b from a graph? Walk me through finding the y-intercept and slope step by step."
If you struggle with tables:"How do I write a slope-intercept equation from a table of x and y values? My table does not include x=0. Show me how to find b using a point."
📺 Learn More
- Khan Academy: Search "slope-intercept form" — watch "Intro to slope-intercept form" and "Writing slope-intercept equations"
- YouTube: Search "slope intercept form from a table Algebra 1"
- Khan Academy practice: Search "slope-intercept form" in Algebra 1 exercises for auto-graded practice