1. 3.5 Slopes of Lines

2. Rise: the difference in the y-values of two points on a line.
Run: the difference in the x-values of two points on a line.
Slope: or
For (x1, y1) and (x2, y2);

3. Examples:
Use the slope formula to determine the slope of each line. 1) 2) 3) 4)

4. A fraction with zero in the denominator is undefined because it is impossible to divide by zero.

6. Example:
Justin is driving from home to his college dormitory. At 4:00 p.m., he is 260 miles from home. At 7:00 p.m., he is 455 miles from home. Graph the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line.

7. Slopes of Parallel and Perpendicular Lines
Parallel Lines Theorem:
Parallel lines have the same slope
Perpendicular Lines Theorem:
Perpendicular lines have slopes that are negative reciprocals. (The slopes have a product of -1)
Vertical and horizontal lines are perpendicular

8. Example:
Decide whether the lines are parallel, perpendicular, or neither.
UV and XY for U(0, 2), V(–1, –1), X(3, 1), and Y(–3, 3)
2) GH and IJ for G(–3, –2), H(1, 2), I(–2, 4), and J(2, –4)
3) CD and EF for C(–1, –3), D(1, 1), E(–1, 1), and F(0, 3)

9. Check it Out! Page 184