<< Chapter < Page Chapter >> Page >

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

( 1 , 4 ) , ( 3 , 9 )

5 2

Got questions? Get instant answers now!

( 0 , 3 ) , ( 4 , 6 )

3 4

Got questions? Get instant answers now!

( 2 , 5 ) , ( 4 , 0 )

5 2

Got questions? Get instant answers now!

( −3 , 3 ) , ( 4 , −5 )

8 7

Got questions? Get instant answers now!

( −2 , 4 ) , ( 3 , −1 )

Got questions? Get instant answers now!

( −1 , −2 ) , ( 2 , 5 )

7 3

Got questions? Get instant answers now!

( −2 , −1 ) , ( 6 , 5 )

Got questions? Get instant answers now!

( 4 , −5 ) , ( 1 , −2 )

−1

Got questions? Get instant answers now!

( 3 , −6 ) , ( 2 , −2 )

Got questions? Get instant answers now!

Graph a Line Given a Point and the Slope

In the following exercises, graph each line with the given point and slope.

( −3 , 4 ) ; m = 3 2

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 4) and (negative 1, 1).

Got questions? Get instant answers now!

( −2 , 5 ) ; m = 5 4

Got questions? Get instant answers now!

( −1 , −4 ) ; m = 4 3

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 1, negative 4) and intercepts the x-axis at (2, 0).

Got questions? Get instant answers now!

( −3 , −5 ) ; m = 3 2

Got questions? Get instant answers now!

y -intercept 3; m = 2 5

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the y-axis at (0, 3) and passes through the point (5, 1).

Got questions? Get instant answers now!

y -intercept 5; m = 4 3

Got questions? Get instant answers now!

x -intercept −2 ; m = 3 4

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the x-axis at (negative 2, 0) and passes through the point (2, 3).

Got questions? Get instant answers now!

x -intercept −1 ; m = 1 5

Got questions? Get instant answers now!

Everyday math

Slope of a roof. An easy way to determine the slope of a roof is to set one end of a 12 inch level on the roof surface and hold it level. Then take a tape measure or ruler and measure from the other end of the level down to the roof surface. This will give you the slope of the roof. Builders, sometimes, refer to this as pitch and state it as an “ x 12 pitch” meaning x 12 , where x is the measurement from the roof to the level—the rise. It is also sometimes stated as an “ x -in-12 pitch”.

  1. What is the slope of the roof in this picture?
  2. What is the pitch in construction terms?
    This figure shows one side of a sloped roof of a house. The rise of the roof is labeled “4 inches” and the run of the roof is labeled “12 inches”.

1 3 4 12 pitch or 4-in-12 pitch

Got questions? Get instant answers now!

The slope of the roof shown here is measured with a 12” level and a ruler. What is the slope of this roof?

This figure shows one side of a sloped roof of a house. The rise of the roof is measured with a ruler and shown to be 7 inches. The run of the roof is measured with a twelve inch level and shown to be 12 inches.
Got questions? Get instant answers now!

Road grade. A local road has a grade of 6%. The grade of a road is its slope expressed as a percent. Find the slope of the road as a fraction and then simplify. What rise and run would reflect this slope or grade?

3 50 ; rise = 3, run = 50

Got questions? Get instant answers now!

Highway grade. A local road rises 2 feet for every 50 feet of highway.

What is the slope of the highway?
The grade of a highway is its slope expressed as a percent. What is the grade of this highway?

Got questions? Get instant answers now!

Wheelchair ramp. The rules for wheelchair ramps require a maximum 1-inch rise for a 12-inch run.

How long must the ramp be to accommodate a 24-inch rise to the door?
Create a model of this ramp.

288 inches (24 feet)  Models will vary.

Got questions? Get instant answers now!

Wheelchair ramp. A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend a ramp.

How long must a ramp be to easily accommodate a 24-inch rise to the door?
Create a model of this ramp.

Got questions? Get instant answers now!

Writing exercises

What does the sign of the slope tell you about a line?

When the slope is a positive number the line goes up from left to right. When the slope is a negative number the line goes down from left to right.

Got questions? Get instant answers now!

How does the graph of a line with slope m = 1 2 differ from the graph of a line with slope m = 2 ?

Got questions? Get instant answers now!

Why is the slope of a vertical line “undefined”?

A vertical line has 0 run and since division by 0 is undefined the slope is undefined.

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has seven rows and four columns. The first row is a header row and it labels each column. The first column is labeled

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Questions & Answers

how to square
Fiona Reply
easiest way to find the square root of a large number?
Jackie
the accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery set up a linear system whose solution provides the unknown flow rates (b) solve the system for the unknown flow rates (c) find the flow rates and directions of flow if x4=50and x6=0
Sabee Reply
What is observation
adeyemi Reply
I'm confused by the question. Can you describe or explain the math question it pertains to?
Melissa
there is no math to it because all you use is your vision or gaze to the sorrounding areas
Cesarp
Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?
Sunnyshay Reply
5 times max
Anton
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 1/3 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
Sophia Reply
35 min
Debra
Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs $9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot?
Parker Reply
what you wanna get
Cesar
800 sq. ft @ $1.50 & 200 sq. ft @ $9.00
Marco
Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16 % of the total - bill as a tip. How much should the tip be?
74.25 × .16 then get the total and that will be your tip
David
$74.25 x 0.16 = $11.88 total bill: $74.25 + $11.88 = $86.13
ericka
yes and tip 16% will be $11.88
David
what is the shorter way to do it
Cesar Reply
Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?
Alexandra Reply
Uno de los ángulos suplementario es 4° más que 1/3 del otro ángulo encuentra las medidas de cada uno de los angulos
Enith Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Alexandra Reply
I hope this is correct, x=cooler 1 5x=cooler 2 x + 5x = 48 6x=48 ×=8 gallons 5×=40 gallons
ericka
Priam has pennies and dimes in a cup holder in his car. The total value of the coins is $4.21 . The number of dimes is three less than four times the number of pennies. How many pennies and how many dimes are in the cup?
Cecilia Reply
Arnold invested $64,000 some at 5.5% interest and the rest at 9% interest how much did he invest at each rate if he received $4500 in interest in one year
Heidi Reply
List five positive thoughts you can say to yourself that will help youapproachwordproblemswith a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.
Elbert Reply
Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?
Leika Reply
324.00
Irene
1.2% of 27.000
Irene
i did 2.4%-7.2% i got 1.2%
Irene
I have 6% of 27000 = 1620 so we need to solve 2.4x +7.2y =1620
Catherine
I think Catherine is on the right track. Solve for x and y.
Scott
next bit : x=(1620-7.2y)/2.4 y=(1620-2.4x)/7.2 I think we can then put the expression on the right hand side of the "x=" into the second equation. 2.4x in the second equation can be rewritten as 2.4(rhs of first equation) I write this out tidy and get back to you...
Catherine
Practice Key Terms 7

Get the best Elementary algebra course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask