01 Key Concepts
Slope-Intercept Form
y = mx + b, where m is the slope (steepness/direction) and b is the y-intercept (where the line crosses the y-axis).
Slope Formula
Given two points (x1,y1) and (x2,y2), slope m = (y2-y1) / (x2-x1) — the 'rise over run'.
Positive, Negative, Zero, and Undefined Slopes
Positive slope rises left to right; negative slope falls left to right; zero slope is a horizontal line; undefined slope is a vertical line.
X-Intercept and Y-Intercept
The x-intercept is where the line crosses the x-axis (where y=0); the y-intercept is where it crosses the y-axis (where x=0).
Point-Slope Form
y - y1 = m(x - x1), useful for writing a line's equation when you know its slope and just one point.
02 Key Formulas
- Slope m = (y2-y1)/(x2-x1)
- Slope-intercept form: y = mx + b
- Point-slope form: y - y1 = m(x - x1)
03 Solved Examples
Example 1 Find the slope of the line through (1,2) and (4,11).
- Apply the slope formula: m = (11-2)/(4-1).
- = 9/3.
Answer: m = 3
Example 2 Find the y-intercept of y = 4x - 7.
- The y-intercept is the constant term b in y = mx + b.
- Here b = -7.
Answer: y-intercept = -7 (the point (0,-7))
Example 3 Write the equation of a line with slope 2 passing through (3,5), using point-slope form, then convert to slope-intercept form.
- Point-slope form: y - 5 = 2(x - 3).
- Distribute: y - 5 = 2x - 6.
- Add 5 to both sides: y = 2x - 1.
Answer: y = 2x - 1
04 Practice Questions
1Find the slope through (0,0) and (3,9).
3
2Find the y-intercept of y = -3x + 8.
8
3Find the slope of a horizontal line.
0
4Find the slope of a vertical line.
Undefined
5Write the point-slope equation for slope 4 through (2,1).
y - 1 = 4(x - 2)
📄 Graphing Lines — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.