Chapter 3

Write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is 6 and the line is perpendicular to the line whose equation is \(y=5 x-1\).

Will help you prepare for the material covered in the next section. Is \(y \leq \frac{2}{3} x\) a true statement for \(x=1\) and \(y=1 ?\)

Make Sense? In Exercises \(57-60\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I visualize slope as walking along a line from left to right. If I'm walking uphill, the slope is positive, and if I'm walking downhill, the slope is negative.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When I write a linear inequality with \(y\) isolated on the left, \(<\) indicates a region that lies below the boundary line.

Graph equation. \(5 y=20\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=x-2$$

Write an equation in the form \(y=m x+b\) of the line that is described. The \(y\) -intercept is 7 and the line is perpendicular to the line whose equation is \(y=8 x-3\).

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I have less than \(\$ 5.00\) in nickels and dimes, so the linear inequality $$0.05 n+0.10 d<5.00$$ models how many nickels, \(n,\) and how many dimes, \(d,\) that I might have.

Graph equation. \(12-3 x=0\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=2 x+1$$

Write an equation in the form \(y=m x+b\) of the line that is described. The line has the same \(y\) -intercept as the line whose equation is \(16 y=8 x+32\) and is parallel to the line whose equation is \(3 x+3 y=9\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The ordered pair \((0,-3)\) satisfies \(y>2 x-3\)

Graph equation. \(12-4 x=0\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=2 x-1$$

Write an equation in the form \(y=m x+b\) of the line that is described. The line has the same \(y\) -intercept as the line whose equation is \(2 y=6 x+8\) and is parallel to the line whose equation is \(4 x+4 y=20\).

In Exercises \(61-64\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The line through \((2,2)\) and the origin has slope 1

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of \(x

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-x+2$$

Write an equation in the form \(y=m x+b\) of the line that is described. The line rises from left to right. It passes through the origin and a second point with equal \(x\) - and \(y\) -coordinates.

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-x+3$$

Write an equation in the form \(y=m x+b\) of the line that is described. The line falls from left to right. It passes through the origin and a second point with opposite \(x\) - and \(y\) -coordinates.

In Exercises \(61-64\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The line through \((3,1)\) and \((3,-5)\) has zero slope.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of \(x<4\) is the half-plane to the left of the vertical line described by \(x=4\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-3 x-1$$

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-3 x-2$$

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=\frac{1}{2} x$$

Describe how to find the slope and the \(y\) -intercept of a line whose equation is given.

Use a graphing utility to graph each equation in Exercises \(67-70\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. $$y=2 x+4$$

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities in $$y \leq 4 x+4$$

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-\frac{1}{2} x$$

Describe how to graph a line using the slope and \(y\) -intercept. Provide an original example with your description.

Use a graphing utility to graph each equation in Exercises \(67-70\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. $$y=-3 x+6$$

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-\frac{1}{4} x$$

A formula in the form \(y=m x+b\) models the cost, \(y,\) of a four-year college \(x\) years after \(2010 .\) Would you expect \(m\) to be positive, negative, or zero? Explain your answer.

Use a graphing utility to graph each equation in Exercises \(67-70\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. $$y=-\frac{1}{2} x-5$$

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities in $$y \geq \frac{1}{2} x+4$$

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=\frac{1}{4} x$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The slope-intercept form of a line's equation makes it possible for me to determine immediately the slope and the \(y\) -intercept.

Use a graphing utility to graph each equation in Exercises \(67-70\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. $$y=\frac{3}{4} x-2$$

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities in $$y \leq-\frac{1}{2} x+4$$

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=\frac{1}{3} x+1$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Because the variable \(m\) does not appear in \(A x+B y=C\) equations in this form make it impossible to determine the line's slope.

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=\frac{1}{3} x-1$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If I drive \(m\) miles in a year, the formula \(c=0.25 m+3500\) models the annual cost, \(c,\) in dollars, of operating my car, so the equation shows that with no driving at all, the cost is \(\$ 3500,\) and the rate of increase in this cost is \(\$ 0.25\) for each mile that I drive.

A 36 -inch board is cut into two pieces. One piece is twice as long as the other. How long are the pieces? (Section 2.5 , Example 2 )

Find the quotient: \(\frac{2}{3} \div\left(-\frac{5}{4}\right)\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-\frac{3}{2} x+1$$

Simplify: \(-10+16 \div 2(-4) .\) (Section 1.8, Example 4)

Evaluate \(x^{2}-4\) for \(x=-3\)

graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-\frac{3}{2} x+2$$