1) -1 – 4 2) 0 – (-2)

4 – ( -3) -1 – (-2)

3) 3 – 4 4) 2 – (-2)

2 + 1 3 – 6

State Standard – 2.0 Students solve systems of linear equations.

Objective – To be able to find the slopes of lines and classify parallel and perpendicular lines.

The Slope Of A Line

The slope of the nonvertical line passing through the points (x1,y1) and (x2,y2) is:

m = = y2 – y1 rise x2 – x1 run

(x1,y1)

(x2,y2)

(y2 – y1)rise

(x2 – x1)run

–5 –4 –3 –2 –1 1 2 543

–5

–4

–3

–2

–1

1

2

5

4

3

Extra Example 3a

Find the slope of the line passing through (-2,-4) and (3,-1).

Solution: Let (x1,y1) = (-2,-4) and (x2,y2) = (3,-1).

m = y2 – y1 x2 – x1

m = -1 – -4 3 – -2

m = -1 + 4 3 + 2

m = 3 5

rises (m>0)

positive slope

Classification Of Lines By Slope

undefined slope

(m is undefined)

negative slope

falls (m<0)

zero slope

(m=0)

Extra Example 3b

Without graphing tell whether the line through the given points rises, falls, is horizontal, or is vertical.

a. (-2,3), (1,5) b. (1, -2) and (3,-2)

m = y2 – y1 x2 – x1

m = 5 – 3 1 – -2

m = 2 3

rises

m = x2 – x1

m = -2 – -2 3 – 1

m = 0

2

horizontal

y2 – y1

Slopes Of Parallel and Perpendicular Lines

Lines are parallel only if they have the same slopes. m1 = m2

Lines are perpendicular only if their slopes are negative reciprocals of each other.

m1 = -1/m2 or m1m2 = -1

Due Tomorrow:

Pg. 69 – 70

11 – 19, 51 – 57, 63, and 64