1. Review of lines Section 2-A

2. Slope (m) of a line Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be points on a nonvertical line, L. The slope of L is

3. Slope measure steepness of a line The steeper the line the greater the absolute value of slope Lines that rise to the right have positive slopes Lines that fall to the right have negative slopes Horizontal lines have zero slopes Vertical lines have undefined slopes

4. Slope = Ratio If the x and y values have the same units, then the slope will have no units If the x and y values have different units, especially when x is in units of time, then slope will have units per time Slope = Rate of Change

5. Equations of lines Consider Multiply both sides by the denominator Point-slope form Suppose point one is The y-intercept (0,b) Slope-intercept form Standard/General form

6. Remember Vertical lines – the value of x does not change Horizontal lines – the value of y does not change and m = 0

7. Parallel (Tangent) and Perpendicular (Normal) Tangent lines – two lines with the same slope Normal lines – two lines that have slopes that are opposite reciprocals

8. 1)Find the equation of the line through (6,8) that is parallel to 3x – 5y = 11 in slope-intercept form

9. 2) Find the equation of the line through the point of intersection of the lines 3x + 4y = 8 and 6x – 10y = 7 that is normal to the first line in General form

10. 3) Find an additional point through the line Choose an arbitrary value for x:

11. HOMEWORK Page 16 # 9,11,12,19,21,29-37, 61-67 all May want to use graph paper