⚠️ Top Mistakes on This Topic
- Forgetting to clear fractions: Before moving terms, multiply ALL terms by the denominator to get integers.
- Leaving A negative: If −2x + 3y = 6, multiply by −1 to get 2x − 3y = −6. A must always be positive.
- Sign errors when moving x-term: y = 3x + 5 → subtract 3x from both sides → −3x + y = 5 → multiply by −1 → 3x − y = −5.
- Reverse conversion (standard → slope-intercept): Isolate y by moving x-term to the right first, then divide by the y-coefficient.
Q1 Easy
y = 2x + 5 → Standard Form
1
Subtract 2x from both sides: −2x + y = 5
2
A = −2 is negative. Multiply by −1: 2x − y = −5
2x − y = −5
Q2 Easy
y = −3x + 6 → Standard Form
1
Add 3x to both sides: 3x + y = 6
2
A = 3 (positive ✓). Done.
3x + y = 6
Q3 Easy
y = x − 4 → Standard Form
1
Subtract x: −x + y = −4
2
Multiply by −1: x − y = 4
x − y = 4
Q4 Medium
y = (1/2)x − 3 → Standard Form
1
Multiply all terms by 2: 2y = x − 6
2
Subtract x: −x + 2y = −6
3
Multiply by −1: x − 2y = 6
x − 2y = 6
Q5 Medium
y = −(2/3)x + 4 → Standard Form
1
Multiply all terms by 3: 3y = −2x + 12
2
Add 2x: 2x + 3y = 12
3
A = 2 (positive ✓). Done.
2x + 3y = 12
Q6 Medium
2x − 6y = 12 → Slope-Intercept Form
1
Subtract 2x: −6y = −2x + 12
2
Divide everything by −6: y = (−2x)÷(−6) + 12÷(−6)
3
Simplify: y = (1/3)x − 2
y = (1/3)x − 2
Q7 Medium
5x + 10y = 20 → Slope-Intercept Form
1
Subtract 5x: 10y = −5x + 20
2
Divide by 10: y = −(1/2)x + 2
y = −(1/2)x + 2
Q8 Medium
Apples $2, pears $3, total $24
1
Cost of apples + cost of pears = total: 2a + 3p = 24
2
A=2 (positive ✓), integers only ✓
2a + 3p = 24
Q9 Hard
Student tickets $5, adult $10, total $200
1
Equation: 5s + 10a = 200 (or simplified: s + 2a = 40)
2
x-int (a=0): 5s = 200 → s = 40 → (40, 0). Meaning: if only students bought tickets, 40 would need to be sold.
3
y-int (s=0): 10a = 200 → a = 20 → (0, 20). Meaning: if only adults bought tickets, 20 would need to be sold.
5s + 10a = 200 | x-int (40,0): 40 student tickets | y-int (0,20): 20 adult tickets
Q10 Hard
Point (3,−1), slope 2 — which standard form equation?
1
Start with slope-intercept: y = 2x + b. Substitute (3,−1): −1 = 2(3) + b → b = −7
2
Equation: y = 2x − 7
3
Convert: subtract 2x → −2x + y = −7 → multiply by −1 → 2x − y = 7
4
That matches option B) 2x − y = 7
Answer: B — 2x − y = 7
🤖 AI Prompts for Topic 4
If you're unsure how to convert forms:"Explain step by step how to convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C). When do I need to multiply to clear fractions? Show me two examples — one without fractions and one with."
If you forgot what standard form rules are:"What are the rules for standard form Ax + By = C in Algebra 1? Does A have to be positive? Can there be fractions? Explain each rule."
If word problems confuse you:"How do I write a standard form equation from a word problem? Give me an example where two items have different prices and there is a total amount."
📺 Learn More
- Khan Academy: Search "standard form for linear equations"
- YouTube: Search "converting slope intercept to standard form Algebra 1"
- YouTube: Search "standard form equations word problems Algebra 1" for word problem practice