Slope: Two points

Pre - Requisite
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 / 8.4.16
8.4.21
8.4.22
Student Learning Goal / ·  Students 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.
·  Students use the slope formula to compute the slope of a non-vertical line.
Media
HW / #62
Spiral Review #18
WKSP

Slope: Two points

Same Slope

Calculate the slope of the line using different pairs of points.

PR / RP
RQ / QR
PQ / QP

All of the slopes are

Exercise: Determine the rate of change of the following lines.

1. / / 2. /

Track the Graph

Sometime, you need to find the points. Keep tracking the graph until you find a ‘friendly’ point.

Find the constant of proportionality of the graph:

Exercise: Find the slope of each of the following graphs:

1. / / 2. /

Given the Slope

Draw a line that passes through the origin and has the following slope:

m = 25
/ m = -25

m = -52
/ m = 212

Given Two Points

A point holds important information. A point (x, y) tells you that when x is a certain value, it produces y.

You are told that a line goes through the points D(-6, 1) and W(-4, 3). Find the slope of the line.

We don’t need to graph points to find the slope! Recall the formula for slope:

m= ∆y∆x

To find the slope of DW, simply find the distance you rise over the distance you run.

The slope of D(-6, 1) and W(-4, 3) =

Exercise: Find the slope of the line given the following points:

1. / (0, 4) and (8, 10) / 2. / (-1, 5) and (2, -3)
3. / (2, -3) and (-4, 5) / 4. / (-2, -3) and (-4, -5)

Make It Real

Erik set his stopwatch to zero and started it at the beginning of his walk. He walks at a constant speed of 3 miles per hour.

Create a table of values where x is the number of hours Erik walks and y is the distance he walks in miles.

t
(hours) / d
(miles)
0
1
2
3

According to the table of values, what rate does Erik walk?

Write an equation to represent this situation.

Exercise:

1. / Faucet A leaks at a constant rate of 7 gallons per hour. Suppose y gallons leak in x hours from 6am. Express the situation as a linear equation in two variables.
Faucet B leaks at a constant rate and the table below shows the number of gallons, y, that leak in x hours.
Hours (x) / Gallons (y)
2 / 13
4 / 26
7 / 45.5
10 / 65
What rate does the second faucet leak?
Which faucet leaks faster?
2. / The graph below represents the constant rate at which Train A travels.

What is the constant rate of travel for Train A?
Train B travels at a constant rate. The train travels at an average rate of 95 miles every one and a half hours. What is the constant rate of travel for Train B?
Which train is traveling at a greater speed?

Name: ______Date: ______

Pre-Algebra Exit Ticket

Find the rate of change of the line.

A certain line has a slope of -12. Name two points that may be on the line.

Name: ______Date: _____

Pre-Algebra HW #62


1. / Find the slope of the following graph:

Review:

2. / Does the graph of the line shown below have a positive or negative slope? Explain.

3. / A pine tree measured 4012 feet tall. Over the next 712 years, it grew to a height of 57 feet. During the 712 years, what was the average yearly growth rate of the height of the tree?