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.

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ok
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