⚠️ Top Mistakes on This Topic
- Flipping which variable to set to zero: x-intercept → set y=0. y-intercept → set x=0. Do NOT mix these up.
- Writing the intercept as just a number: Always write as a coordinate pair: (4, 0) not just "4".
- Sign errors with negative coefficients: In −3y = 12, divide both sides by −3 to get y = −4, not y = 4.
- Q10 type — forgetting to convert to standard form: Standard form requires Ax + By = C with A positive and no fractions.
Q1 Easy
2x + y = 8
1
x-int (y=0): 2x = 8 → x = 4 → (4, 0)
2
y-int (x=0): y = 8 → (0, 8)
x-int: (4, 0) y-int: (0, 8)
Q2 Easy
x + 3y = 9
1
x-int (y=0): x = 9 → (9, 0)
2
y-int (x=0): 3y = 9 → y = 3 → (0, 3)
x-int: (9, 0) y-int: (0, 3)
Q3 Easy
6x − 2y = 12
1
x-int (y=0): 6x = 12 → x = 2 → (2, 0)
2
y-int (x=0): −2y = 12 → y = −6 → (0, −6)
x-int: (2, 0) y-int: (0, −6)
Q4 Medium
4x + 5y = 20
1
x-int (y=0): 4x = 20 → x = 5 → (5, 0)
2
y-int (x=0): 5y = 20 → y = 4 → (0, 4)
x-int: (5, 0) y-int: (0, 4)
Q5 Medium
3x − 4y = 24
1
x-int (y=0): 3x = 24 → x = 8 → (8, 0)
2
y-int (x=0): −4y = 24 → y = −6 → (0, −6)
x-int: (8, 0) y-int: (0, −6)
Q6 Medium
−2x + 4y = 8
1
x-int (y=0): −2x = 8 → x = −4 → (−4, 0)
2
y-int (x=0): 4y = 8 → y = 2 → (0, 2)
x-int: (−4, 0) y-int: (0, 2)
Q7 Medium
2x + 3y = 12 — find intercepts and graph
1
x-int (y=0): 2x = 12 → x = 6 → (6, 0)
2
y-int (x=0): 3y = 12 → y = 4 → (0, 4)
3
Plot (6, 0) on x-axis and (0, 4) on y-axis. Draw a straight line through both points.
x-int: (6, 0) y-int: (0, 4)
Q8 Medium
4x − 2y = 8
1
x-int (y=0): 4x = 8 → x = 2 → (2, 0)
2
y-int (x=0): −2y = 8 → y = −4 → (0, −4)
x-int: (2, 0) y-int: (0, −4)
Q9 Hard
5x + 3y = −15
1
x-int (y=0): 5x = −15 → x = −3 → (−3, 0)
2
y-int (x=0): 3y = −15 → y = −5 → (0, −5)
3
Both intercepts are negative. On a graph: the x-intercept is to the LEFT of the origin, and the y-intercept is BELOW the origin. The entire line runs through the 3rd and 4th quadrants.
x-int: (−3, 0) y-int: (0, −5)
Q10 Hard
x-int: (4, 0) and y-int: (0, 6) → write in standard form
1
Find slope using the two points: m = (6−0)÷(0−4) = 6÷(−4) = −3/2
2
b = 6 (y-intercept is given). So: y = −(3/2)x + 6
3
Multiply all terms by 2: 2y = −3x + 12
4
Move x-term to left: 3x + 2y = 12
5
Check: A=3 (positive ✓), no fractions ✓
3x + 2y = 12
🤖 AI Prompts for Topic 3
If you mix up x and y intercepts:"I keep confusing x-intercepts and y-intercepts. Can you give me a memory trick for remembering which variable to set to zero for each one?"
If Q10 type questions confuse you:"How do I write a standard form equation Ax + By = C when I'm only given the x-intercept and y-intercept? Walk me through it step by step."
If you want to understand intercepts visually:"Can you describe what x and y intercepts look like on a graph and explain why they are useful for drawing a line quickly?"
📺 Learn More
- Khan Academy: Search "x-intercepts and y-intercepts from standard form"
- YouTube: Search "how to find x and y intercepts standard form Algebra 1"
- Khan Academy: Search "graphing using intercepts" for practice with graphing