4.4 Understand slope of a line  (Page 7/14)

 Page 7 / 14

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

$y=3$

0

$y=1$

$x=4$

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$x=2$

$y=-2$

0

$y=-3$

$x=-5$

undefined

$x=-4$

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.

$\left(1,4\right),\left(3,9\right)$

$\frac{5}{2}$

$\left(2,3\right),\left(5,7\right)$

$\left(0,3\right),\left(4,6\right)$

$\frac{3}{4}$

$\left(0,1\right),\left(5,4\right)$

$\left(2,5\right),\left(4,0\right)$

$-\frac{5}{2}$

$\left(3,6\right),\left(8,0\right)$

$\left(-3,3\right),\left(4,-5\right)$

$-\frac{8}{7}$

$\left(-2,4\right),\left(3,-1\right)$

$\left(-1,-2\right),\left(2,5\right)$

$\frac{7}{3}$

$\left(-2,-1\right),\left(6,5\right)$

$\left(4,-5\right),\left(1,-2\right)$

$-1$

$\left(3,-6\right),\left(2,-2\right)$

Graph a Line Given a Point and the Slope

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

$\left(1,-2\right)$ ; $m=\frac{3}{4}$ $\left(1,-1\right)$ ; $m=\frac{2}{3}$

$\left(2,5\right)$ ; $m=-\frac{1}{3}$ $\left(1,4\right)$ ; $m=-\frac{1}{2}$

$\left(-3,4\right)$ ; $m=-\frac{3}{2}$ $\left(-2,5\right)$ ; $m=-\frac{5}{4}$

$\left(-1,-4\right)$ ; $m=\frac{4}{3}$ $\left(-3,-5\right)$ ; $m=\frac{3}{2}$

y -intercept 3; $m=-\frac{2}{5}$ y -intercept 5; $m=-\frac{4}{3}$

x -intercept $-2$ ; $m=\frac{3}{4}$ x -intercept $-1$ ; $m=\frac{1}{5}$

$\left(-3,3\right)$ ; $m=2$ $\left(-4,2\right)$ ; $m=4$

$\left(1,5\right)$ ; $m=-3$ $\left(2,3\right)$ ; $m=-1$

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 $\frac{x}{12}$ , 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? $\frac{1}{3}$ 4 12 pitch or 4-in-12 pitch

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

$\frac{3}{50}$ ; rise = 3, run = 50

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?

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.

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.

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.

How does the graph of a line with slope $m=\frac{1}{2}$ differ from the graph of a line with slope $m=2$ ?

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.

Self check

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

a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs $6.04 per gallon and the soda costs$4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs $5.71 per gallon? Mohamed Reply (a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r) muhammad Reply 4x-7y=8 2x-7y=1 what is the answer? Ramil Reply x=7/2 & y=6/7 Pbp x=7/2 & y=6/7 use Elimination Debra true bismark factoriz e usman 4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2 Peggie Ok cool answer peggie Frank thanks Ramil copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x Sandra Reply What is c+4=8 Penny Reply 2 Letha 4 Lolita 4 Rich 4 thinking C+4=8 -4 -4 C =4 thinking I need to study Letha 4+4=8 William During two years in college, a student earned$9,500. The second year, she earned $500 more than twice the amount she earned the first year. Nicole Reply 9500=500+2x Debra 9500-500=9000 9000÷2×=4500 X=4500 Debra X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500 Pbp Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles. Josh Reply Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than$500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and for a package the cost is$7.
hey
Juan
Sup
patrick
The sum of two numbers is 155. The difference is 23. Find the numbers
The sum of two numbers is 155. Their difference is 23. Find the numbers
Michelle
The difference between 89 and 66 is 23
Ciid
Joy is preparing 20 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?
hello
bismark
I need a math tutor BAD
Stacie
Me too
Letha
me too
Xavier
ok
Bishal
teet
Bishal
Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone, it would take her 120 days. How long would it take Deb to write the book alone?
Tell Deb to write the book alone and report back on how long it took her. Deb could get bored and stop, she could get sick next week and prolong the time, she could die next month. This question is impossible to answer.
vV
right*
tyler
is there a thumbs up mathematical symbol in algebra? 👍²= vV 90days x 120days =10800 120days - 90days = 30 10800days/30days= 360days? (ad) derall=1440 mins (90x ad )+(120 x ad )/(120 x ad ))-((90d x ad)= you go glen coco! I'll see my self out
Nick
Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?
6.25
Ciid
6.25
Big
?
Twila
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
Ciid
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.
tyler
H=57 and O=285 figure out what the adjacent?
tyler
help
Twila
draw a diagram first
John
Amara currently sells televisions for company A at a salary of $17,000 plus a$100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a$20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000 17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000
Ciid  By  By Anonymous User   By   