SAT Math: Slope-Intercept Form (y = mx + b)
44+ practice questions in Praczo
The concept, explained
- 1
In y = mx + b, m is the slope (rate of change) and b is the y-intercept (the value of y when x = 0). Memorize these roles — the SAT tests them constantly in context.
- 2
To find the slope from two points, use m = (y₂ − y₁) / (x₂ − x₁). Always subtract in the same order — numerator and denominator must use the same point as "point 1."
- 3
To write the equation from a graph: read the y-intercept directly (where the line crosses the y-axis), then use rise/run between two clear points to find the slope.
- 4
To write the equation given a slope and one point, substitute into y = mx + b and solve for b, then rewrite the full equation with numbers.
- 5
Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals — if one has slope 2, the other has slope −½.
- ✗ Mixing up m and b: in y = 3x + 5, the slope is 3 and the y-intercept is 5 — not the other way around.
- ✗ Calculating slope as run/rise instead of rise/run. Slope = vertical change ÷ horizontal change.
SAT-style practice
A delivery driver charges a flat fee of (8.00 plus )2.50 per mile. Which equation represents the total charge y, in dollars, for a trip of x miles?
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