The Slope Of A LineObjective: To find the slope of a line and to

graph a line given its slope and a point.

What is slope?• There are several definitions,

but they are all related.

• Rate of change

21

21

xx

yyRun

Rise

Example

y

x

Distancein miles

TimeIn hours

(x1,y1)

(x2,y2)

run = x1 – x2

rise = y1 – y2

m = rise/run = (y1 – y2)/(x1 – x2) = miles/hour

Find the slope between the two points

• (2, 4) and (5, 1)• (-3, 1) and (6, 4)• (2, 3) and (-1, 3)• (-2, 5) and (-2, 7)

• m = -1• m = 1/3• m = 0• No slope or undefined

slope

Theorem• The slope of a line in standard form

Ax + By = C is -A/B

Point Slope Form• y – y1 = m(x – x1)

• Variation: y = y1 + (x – x1)m

Graph The Line Passing Through (1,2) with a slope m = ¼

• Start by graphing the point (1,2)

• Since slope is rise over run move up 1 unit and right 4 units

-4 -3 -2 -1

4321

1 2 3 4 5 6-1-2-3-4