SAT Math: Work with standard form (Ax + By = C)
26+ practice questions in Praczo
The concept, explained
- 1
Standard form is Ax + By = C, where A, B, C are usually integers and A is non-negative.
- 2
From standard form, slope = -A/B and y-intercept = C/B. Memorize these — they save time on conversion questions.
- 3
Fast intercepts: set x = 0 to get y-intercept (0, C/B); set y = 0 to get x-intercept (C/A, 0).
- 4
To convert slope-intercept y = mx + b to standard form, move the x term to the left: -mx + y = b, then multiply through so A is a positive integer.
- 5
Standard form is especially useful in real-world problems where each variable represents a count/quantity (e.g., 2x + 3y = 30 for dollars spent on two items).
- ✗ Forgetting the negative sign in slope = -A/B and using A/B instead.
- ✗ Failing to clear fractions when converting to standard form — SAT answers usually use integer coefficients.
- ✗ Switching the roles of intercepts (using C/A for the y-intercept).
SAT-style practice
What is the slope of the line 3x + 4y = 12?
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