Why this matters for FAST: Slope-intercept form is fundamental to linear relationships. FAST tests require students to find slope from graphs, tables, and word problems, write equations, and interpret slope and y-intercept in real-world contexts.
Students calculate run/rise instead of rise/run, or confuse which direction is positive.
"Slope is RISE over RUN - vertical change over horizontal change. Think: 'Rise comes first, just like in the alphabet R comes before R-un.' Rise = up/down (vertical), Run = left/right (horizontal)."
Students confuse slope (m) with y-intercept (b) in y = mx + b.
"In y = mx + b, the number MULTIPLIED by x is the slope (m), and the number ADDED at the end is the y-intercept (b). Think: 'm goes with x' and 'b stands alone.'"
Students don't understand that negative slope means the line goes down from left to right.
"Positive slope = line goes UP like climbing a hill. Negative slope = line goes DOWN like a slide. Think of walking left to right along the line."
"Slope measures the STEEPNESS of a line - how fast it goes up or down. It's the rate of change: how much y changes when x changes by 1. We calculate it as rise over run: m = (y2 - y1)/(x2 - x1)."
Slope Formula: m = rise/run = (y2 - y1)/(x2 - x1)
Example: Points (1, 2) and (3, 8)
m = (8-2)/(3-1) = 6/2 = 3
Y-Intercept (b): Where the line crosses the y-axis
This is the value of y when x = 0
In real-world contexts, it's often the "starting value"
y = mx + b
m = slope (rate of change)
b = y-intercept (starting value)
Example: y = 3x - 2 has slope 3 and y-intercept -2
Graph y = 2x + 1
1. Plot the y-intercept: (0, 1)
2. Use slope m = 2 = 2/1: From (0, 1), go up 2 and right 1
3. Plot second point: (1, 3)
4. Draw the line through both points
Example: A plumber charges $50 plus $40 per hour. Equation: y = 40x + 50
"Write the equation of a line with slope 4 and y-intercept -3."
Solution: y = 4x - 3