Slope: A Graphic Introduction

Pre - Requisite / Graph a Point
Compare fractions
Standard / 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane, derive the equation y=mx for a line through the origin and the equation y = mx + b of a line intercepting the vertical axis at b.
CC Lesson / 8.4.15
Student Learning Goal /
  • Students know slope is a number that describes the steepness or slant of a line.
  • Students interpret the unit rate as the slope of a graph.

Media / Wind-up toy & ramp
HW / #61
Spiral Review #18
WKSP

Slope: A Graphic Introduction

Steepness (incline)

Graph AGraph B

Which graph is steeper?

Write directions that explains how to move from the origin to the other point on the line for each graph.

Graph A:

Graph B:

Write the directions as ratios, and then compare the ratios.

Graph AGraph B

How does this relate to which graph was steeper?

Exercise:

1. / Graph AGraph B

  1. Which graph is steeper?
  1. Write directions that explains how to move from one point to the other.
Graph A:
Graph B:
  1. Write the directions from part (b) as ratios, and then compare the ratios.

2. / Graph AGraph B

  1. Which graph is steeper?
  1. Write directions that explains how to move from one point to the other
Graph A:
Graph B:
  1. Write the directions from part (b) as ratios , and then compare the ratios.

Direction


Slope
()

What do vectors and slopes of incline have in common?

Exercise: Identify the type of slope find the slope of the following non-vertical lines.

1.

2.

3.Choose a second point … / 4. Choose a second point …

Make It Real

Pauline mows a lawn at a constant rate. Suppose she mowed a 35 square foot lawn in 2.5 minutes.

t (time in
minutes) / linear equation: / A (area in
square feet)
0
1
2.5
5
7.5

What is the slope of this line?

What is the unit rate of mowing the lawn?

Exercise:

A copy machine makes copies at a constant rate. The machine can make 80 copies in minutes.

How many copies can the machine make each minute; that is, what is the unit rate of the copy machine?

Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line?

Slope Unit Rate Rate of Change Steepness of Line Constant of Proportionality

Name: ______Date: ______

Pre-AlgebraExit Ticket

Graph A
/ Graph B

Are both slopes positive or negative?

What is the slope of Graph A?

What is the slope of Graph B?

Compare Graph A to Graph B.

Name: ______Date: _____

Pre-AlgebraHW #61


1. / What is the slope of the following non-vertical lines?
a. b.

Review:

2. / Find at least three solutions to the equation y = 3x – 1, and graph the solutions as points on the coordinate plane. Use a straight edge to connect the points in order to make a (straight) line.

3. / Sammy drew a rectangle that was w inches wide. The expression 2(2w) + 2(w) represents the perimeter of the rectangle that Sammy drew. Which statement relates the perimeter to the width of the rectangle?
  1. The perimeter is 6 inches more than the width.
  2. The perimeter is 6 times the width.
  3. The perimeter is 2 inches more than the width.
  4. The perimeter is 2 times the width.