# 11.4 Understand slope of a line  (Page 7/9)

 Page 7 / 9

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

$-\frac{8}{5}$

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

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

$\frac{7}{3}$

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

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

−1

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

Graph a Line Given a Point and the Slope

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

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

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

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

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

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

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

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

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

$\left(0,3\right);m=-\frac{2}{5}$

$\left(0,5\right);m=-\frac{4}{3}$

$\left(-2,0\right);m=\frac{3}{4}$

$\left(-1,0\right);m=\frac{1}{5}$

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

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

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

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

Solve Slope Applications

In the following exercises, solve these slope applications.

Slope of a roof A fairly easy way to determine the slope is to take a $\text{12-inch}$ level and set it on one end on the roof surface. Then take a tape measure or ruler, and measure from the other end of the level down to the roof surface. You can use these measurements to calculate the slope of the roof. What is the slope of the roof in this picture?

$\frac{1}{3}$

What is the slope of the roof shown?

Road grade A local road has a grade of $\text{6%}.$ The grade of a road is its slope expressed as a percent.

1. Find the slope of the road as a fraction and then simplify the fraction.
2. What rise and run would reflect this slope or grade?

$\phantom{\rule{0.2em}{0ex}}\frac{3}{50}\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}\text{rise}=3;\phantom{\rule{0.2em}{0ex}}\text{run}=50$

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

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

## Everyday math

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

1. How long must the ramp be to accommodate a $\text{24-inch}$ rise to the door?
2. Draw a model of this ramp.

1. 288 inches (24 feet)
2. Models will vary.

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

1. How long must the ramp be to easily accommodate a $\text{24-inch}$ rise to the door?
2. Draw a model of this ramp.

## Writing exercises

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

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?

Explain how you can graph a line given a point and its slope.

## 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?

## Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

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

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

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

1. $\phantom{\rule{0.2em}{0ex}}\left(-1,-5\right)$
2. $\phantom{\rule{0.2em}{0ex}}\left(-3,4\right)$
3. $\phantom{\rule{0.2em}{0ex}}\left(2,-3\right)$
4. $\phantom{\rule{0.2em}{0ex}}\left(1,\frac{5}{2}\right)$

1. III
2. II
3. IV
4. I

1. $\phantom{\rule{0.2em}{0ex}}\left(3,-2\right)$
2. $\phantom{\rule{0.2em}{0ex}}\left(-4,-1\right)$
3. $\phantom{\rule{0.2em}{0ex}}\left(-5,4\right)$
4. $\phantom{\rule{0.2em}{0ex}}\left(2,\frac{10}{3}\right)$

Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

1. (5,3)
2. (2,−1)
3. (−3,−2)
4. (−1,4)

1. (2,0)
2. (0,−5)
3. (−4,0)
4. (0,3)

Verify Solutions to an Equation in Two Variables

In the following exercises, find the ordered pairs that are solutions to the given equation.

show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
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Abdullahi
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find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
16
Makan
x=16
Makan
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hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
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Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
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Need help solving this problem (2/7)^-2
x+2y-z=7
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-1
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s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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