



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.
Graph a Line Given a Point and the Slope
In the following exercises, graph each line with the given point and slope.
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 “
$x$ in12 pitch”.

ⓐ What is the slope of the roof in this picture?

ⓑ What is the pitch in construction terms?
ⓐ
$\frac{1}{3}$
ⓑ 4 12 pitch or 4in12 pitch
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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
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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?
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Wheelchair ramp. The rules for wheelchair ramps require a maximum 1inch rise for a 12inch run.
ⓐ How long must the ramp be to accommodate a 24inch rise to the door?
ⓑ Create a model of this ramp.
ⓐ 288 inches (24 feet)
ⓑ Models will vary.
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Wheelchair ramp. A 1inch rise for a 16inch run makes it easier for the wheelchair rider to ascend a ramp.
ⓐ How long must a ramp be to easily accommodate a 24inch rise to the door?
ⓑ Create a model of this ramp.
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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.
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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?
Questions & Answers
65r to the 4th power50r cubed15r squared+8r+23 ÷ 5r
write in this form a/b answer should be in the simplest form 5%
convert to decimal 9/11
August
Equation in the form of a pending point
y+2=1/6(×4)
write in simplest form 3 4/2
August
definition of quadratic formula
From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
Melissa
what is the answer of w2.6=7.55
w = 10.15
You add 2.6 to both sides and then solve for w (2.6 zeros out on the left and leaves you with w= 7.55 + 2.6)
Korin
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?
greater than $110,000
Michael
Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?
$1.38 worth of strawberries + $1.14 worth of blueberries which= $2.52
Leitha
8 pound of blueberries and 22 pounds of strawberries
Melissa
8 pounds x 4.5 = 36
22 pounds x 1.80 = 39.60
36 + 39.60 = 75.60
75.60 / 30 = average 2.52 per pound
Melissa
8 pounds x 4.5 equal 36
22 pounds x 1.80 equal 39.60
36 + 39.60 equal 75.60
75.60 / 30 equal average 2.52 per pound
Melissa
8 pounds x 4.5 = 36
22 pounds x 1.80 = 39.60
36 + 39.60 = 75.60
75.60 / 30 = average 2.52 per pound
Melissa
The question asks how many pounds of each in order for her to have an average cost of $2.52. She needs 30 lb in all so 30 pounds times $2.52 equals $75.60. that's how much money she is spending on the fruit. That means she would need 8 pounds of blueberries and 22 lbs of strawberries to equal 75.60
Melissa
nawal let's do another😊
Leitha
we can't use emojis...I see now
Leitha
Sorry for the multi post. My phone glitches.
Melissa
Vina has $4.70 in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin does she have?
10 quarters
16 dimes
12 nickels
Leitha
A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet.
wtf. is a tail wind or headwind?
Robert
48 miles per hour with headwind
and
68 miles per hour with tailwind
Leitha
average speed is 58 mph
Leitha
Into the wind (headwind), 125 mph; with wind (tailwind), 175 mph. Use time (t) = distance (d) ÷ rate (r). since t is equal both problems, then 1210/(x25) = 1694/(×+25). solve for x gives x=150.
bruce
the jet will fly 9.68 hours to cover either distance
bruce
Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs $3.50 per pound. How much of each seed should he buy so that the overall cost will be $4.02 per pound?
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?
2q=n
((2q).05) + ((q).25) = 8.75
.1q + .25q = 8.75
.35q = 8.75
q = 25 quarters
2(q)
2 (25)
= 50 nickles
Answer check
25 x .25 = 6.25
50 x .05 = 2.50
6.25 + 2.50 = 8.75
Melissa
John has $175 in $5 and $10 bills in his drawer. The number of $5 bills is three times the number of $10 bills. How many of each are in the drawer?
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
16 goes into 80 5times
while 20 goes into 80 4times and is 4mph faster
Robert
Source:
OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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