Chapter 3

The grade of a road or ramp refers to its slope expressed as a percent. Use this information to solve Exercises \(49-50\). A college campus goes beyond the standards described in Exercise \(49 .\) All wheelchair ramps on campus are designed so that every vertical rise of 1 foot is accompanied by a horizontal run of 14 feet. What is the grade of such a ramp? Round to the nearest tenth of a percent.

Graph equation. \(x=2\)

What is a linear inequality in two variables? Provide an example with your description.

find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-10 x$$

Excited about the success of celebrity stamps, post office officials were rumored to have put forth a plan to institute two new types of thermometers. On these new scales, \(^{\circ} E\) represents degrees Elvis and \(^{\circ} M\) represents degrees Madonna. If it is known that \(40^{\circ} E=25^{\circ} M, 280^{\circ} E=125^{\circ} M\) and degrees Elvis is linearly related to degrees Madonna, write an cquation expressing \(E\) in terms of \(M.\)

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned}&y=x+3\\\&y=-x+1\end{aligned}$$

Graph equation. \(x=4\)

How do you determine whether an ordered pair is a solution of an inequality in two variables, \(x\) and \(y ?\) What is a half-plane?

find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-20 x$$

Use a graphing utility to graph \(y=1.75 x-2 .\) Select the best viewing rectangle possible by experimenting with the range settings to show that the line's slope is \(\frac{7}{4}\).

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned}&y=x+2\\\&y=-x-1\end{aligned}$$

Describe how to calculate the slope of a line passing through two points.

Graph equation. \(x+1=0\)

What does a solid line mean in the graph of an inequality?

find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=8 x-5$$

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{array}{r}x-2 y=2 \\\2 x-4 y=3\end{array}$$

What does it mean if the slope of a line is zero?

Graph equation. \(x+5=0\)

What does a dashed line mean in the graph of an inequality?

find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=6 x-4$$

How many sheets of paper, weighing 2 grams each, can be put in an envelope weighing 4 grams if the total weight must not exceed 29 grams? (Section \(2.7,\) Example 11 ).

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned}x-3 y &=9 \\\3 x-9 y &=18\end{aligned}$$

What does it mean if the slope of a line is undefined?

Graph equation. \(y-3.5=0\)

Explain how to graph \(2 x-3 y<6\)

find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-3 x+7$$

List all the natural numbers in this set: $$\left\\{-2,0, \frac{1}{2}, 1, \sqrt{3}, \sqrt{4}\right\\}$$ (Section \(1.3,\) Example 5 )

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{array}{r}2 x-y=-1 \\\x+2 y=-6\end{array}$$

If two lines are parallel, describe the relationship between their slopes.

Graph equation. \(y-2.5=0\)

Explain how to graph \(2 x-3 y<6\)

find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=-5 x+9$$

Use intercepts to graph \(3 x-5 y=15.\) (Section 3.2, Example 4)

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{array}{r}3 x-y=-2 \\\x+3 y=-9\end{array}$$

If two lines are perpendicular, describe the relationship between their slopes.

Graph equation. \(x=0\)

Compare the graphs of \(3 x-2 y>6\) and \(3 x-2 y \leq 6\) Discuss similarities and differences between the graphs.

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x$$

Will help you prepare for the material covered in the next section. Is \(2 x-3 y \geq 6\) a true statement for \(x=3\) and \(y=-1 ?\)

In Exercises \(57-64\), write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is 5 and the line is parallel to the line whose equation is \(3 x+y=6\).

Make Sense? In Exercises \(57-60\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When finding the slope of the line passing through \((-1,5)\) and \((2,-3),\) I must let \(\left(x_{1}, y_{1}\right)\) be \((-1,5)\) and \(\left(x_{2}, y_{2}\right)\) be \((2,-3)\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. By looking at a linear inequality in two variables, I can immediately determine whether the boundary line of its graph should be solid or dashed.

Graph equation. \(y=0\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x+1$$

Write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is \(-4\) and the line is parallel to the line whose equation is \(2 x+y=8\).

Will help you prepare for the material covered in the next section. Is \(2 x-3 y \geq 6\) a true statement for \(x=0\) and \(y=0 ?\)

Make Sense? In Exercises \(57-60\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When applying the slope formula, it is important to subtract corresponding coordinates in the same order.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The inequality \(2 x-3 y<6\) contains a "less than" symbol, so its graph lies below the boundary line.

Graph equation. \(3 y=9\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x-1$$