1.10 Lines
Ideas in this lesson
- Compute and read slopes
- Write lines from points and slopes
- Use slope-intercept form and line families
- Handle horizontal and vertical lines
- Reason about parallel and perpendicular lines
- Connect standard form and intercepts
- Interpret and build linear rate models
- Use slopes to justify coordinate geometry
- Graph and analyze parameterized line families
- Construct perpendicular bisectors and circle tangents
- Derive intercept form and justify coordinate arguments
- Build and interpret physically restricted linear models
Compute and read slopes · Worked example
The line through \((-2,3)\) and \((2,3)\) is compared with the line through \((2,-2)\) and \((2,2)\). Which statement is correct?
Answer: The first slope is 0; the second slope is undefined.
For the first line, \(\Delta y=0\) and \(\Delta x=4\), so slope is 0.
For the second line, \(\Delta x=0\) and the vertical change is nonzero.
Division by zero is undefined; a vertical line has no finite slope.
For the second line, \(\Delta x=0\) and the vertical change is nonzero.
Division by zero is undefined; a vertical line has no finite slope.