Two Variables, One Line
y = mx + d
Find a line's slope and where it crosses the y-axis from y = mx + d.
In y = mx + d, m is the slope and d is the y-intercept: the line crosses the y-axis at (0, d).
Why m is the slope: (y2 – y1)/(x2 – x1) = (mx2 + d – mx1 – d)/(x2 – x1) = m. The d's cancel.
From standard form, get y on its own. 5x + y = 3 becomes y = –5x + 3: slope –5 (down 5 for each 1 to the right), intercept 3.
Two special lines:
- zero slope: y = 5 is horizontal (no rise at all);
- undefined slope: x = 2 is vertical: the run is 0, and we cannot divide by 0.
The x-intercept of y = mx + c is x = –c/m (put y = 0).
Read the numbers in a story. y = 3x for a filling tank means 3 cm per minute, starting from 0. F = 9C/5 + 32 has slope 9/5 and intercept 32 (0 °C = 32 °F).
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