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

$\left(\mathrm{-3},3\right),\left(2,\mathrm{-5}\right)$

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

$\left(\mathrm{-1},\mathrm{-2}\right),\left(2,5\right)$

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

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

$\left(3,\mathrm{-6}\right),\left(2,\mathrm{-2}\right)$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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?

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?

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.

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.

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.

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

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

1. ⓐ $(\mathrm{-1},\mathrm{-5})$
2. ⓑ $(\mathrm{-3},4)$
3. ⓒ $\left(2,\mathrm{-3}\right)$
4. ⓓ $\left(1,\frac{5}{2}\right)$

1. ⓐ $\left(3,\mathrm{-2}\right)$
2. ⓑ $\left(\mathrm{-4},\mathrm{-1}\right)$
3. ⓒ $\left(\mathrm{-5},4\right)$
4. ⓓ $\left(2,\frac{10}{3}\right)$