1 Slope MATH8 2016­17.notebook January 05, 2017

RISE

RUN

Warm­Up:1.) 4 ­ (­5)

5 ­ 82.) ­10 ­ 11

3 ­ (­4)

Unit 5 Lesson 1: Slope of a Line

COORDINATE PLANE or

Cartesian Plane

Ordered Pairs... ( ___________ , ____________ )

QUADRANTS

( , ) ( , )

( , ) ( , )

1 Slope MATH8 2016­17.notebook January 05, 2017

Finding the Slope of a Line

linear equations: equations whose solutionsfall on a _______ in the coordinate plane.

slope of a line: the _______ of a line; ___________ of a line. The _________ the absolute value of the slope, the more ________ the line will be.

Slope is denoted by using the letter m.

slope = vertical change = change in y horizontal change change in x

If the slope between any 2 points is always the same, then the rate of change is constant ­ a linear relationship.

A line with a POSITIVE SLOPE slants "up hill" or rises from left to right.

m > 0

A line with a NEGATIVE SLOPE slants " down hill" or falls from left to right.

m < 0graphics courtesy of Oswego City School District Regents Exam Prep Center

A line with a ZERO SLOPE is horizontal.

m = 0

A line with an UNDEFINED SLOPE is vertical.

m is undefined

1 Slope MATH8 2016­17.notebook January 05, 2017

• Positive Slope• Increasing• Rises• Slants "up hill"

• Negative Slope• Decreasing• Falls• Slants "down hill"

• Zero Slope• Horizontal• Constant• y­values of coordinates the same

• Undefined Slope• Vertical• Constant• x­values of coordinates the same

Find the slope of the line, given the graph of the line.

1 Slope MATH8 2016­17.notebook January 05, 2017

SUPPOSE you need to find the slope of the line containing the points (1, 6) and (­3, 4) but your not given the graph or graph paper.

FORMULA TO FIND THE SLOPE OF A LINE GIVEN TWO POINTS

The slope, m, of the line through points (x 1, y1) and (x2, y2) is given by...

(1, 6) and (­3, 4) Example:

Another Example:

How do you find the slope of a line given two points on the line?

(0, ­5) and (­2, 5)

a.) (3, ­4), (1, ­6) b.) (­3, 6) (5, 7)

c.) (2, 4) (­5, 4) d.) (2, ­1), (2, 5)

e.) (3, 7)(2, 3) f.) (0, ­1)(5, 3)

Without graphing, tell whether the line through the given points rises, falls, is horizontal or is vertical. (Use the slope formula)

1 Slope MATH8 2016­17.notebook January 05, 2017

Homework ~