Chapter 3

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((-1,5)\) and is perpendicular to the line whose equation is \(x=6\)

In Exercises \(57-64\), 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 \(3 x+3 y=9\)

Graph each 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 slope-intercept form of the line satisfying the given conditions. The line passes through \((-2,6)\) and is perpendicular to the line whose equation is \(x=-4\)

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

In Exercises \(57-64\), 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 \(4 x+4 y=20\)

Graph each 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 slope-intercept form of the line satisfying the given conditions. The line passes through \((-6,4)\) and is perpendicular to the line that has an \(x\) -intercept of 2 and a \(y\) -intercept of \(-4\)

In Exercises \(57-64\), 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. $$y=-x+2$$

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((-5,6)\) and is perpendicular to the line that has an \(x\) -intercept of 3 and a \(y\) -intercept of \(-9\).

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

In Exercises \(57-64\), 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.

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 slope-intercept form of the line satisfying the given conditions. The line is perpendicular to the line whose equation is \(3 x-2 y=4\) and has the same y-intercept as this line.

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

Write an equation in slope-intercept form of the line satisfying the given conditions. The line is perpendicular to the line whose equation is \(4 x-y=6\) and has the same \(y\) -intercept as this line.

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

Use a graphing utility to graph each equation.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. $$y=2 x+4$$

Write an equation in slope-intercept form of the line satisfying the given conditions. What is the slope of a line that is parallel to the line whose equation is \(A x+B y=C, B \neq 0 ?\)

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

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

Use a graphing utility to graph each equation.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. $$y=2 x+4$$

Write an equation in slope-intercept form of the line satisfying the given conditions. What is the slope of a line that is perpendicular to the line whose equation is \(A x+B y=C, A \neq 0\) and \(B \neq 0 ?\)

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

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

Use a graphing utility to graph each equation.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. $$y=-\frac{1}{2} x-5$$

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.

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

Use a graphing utility to graph each equation.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. $$y=\frac{3}{4} x-2$$

Make Sense? In Exercises \(70-73\), determine whether each statement "makes sense" or "does not make sense" and explair 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.

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

Describe how to write the equation of a line if its slope and a point on the line are known.

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

A 36 -inch board is cut into two pieces. One picce is twice as long as the other. How long are the pieces?

Describe how to write the equation of a line if two points on the line are known.

Make Sense? In Exercises \(70-73\), determine whether each statement "makes sense" or "does not make sense" and explair 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.

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. I use \(y=m x+b\) to write equations of lines passing through two points when neither contains the \(y\) -intercept.

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

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. In many examples, I use the slope-intercept form of a line's equation to obtain an equivalent equation in point-slope form.

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

Will help you prepare for the material covered in the next section. From \((0,-3),\) move 4 units up and 1 unit to the right. What point do you obtain?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I have linear models that describe changes for men and women over the same time period. The models have the same slope, so the graphs are parallel lines, indicating that the rate of change for men is the same as the rate of change for women.

In Exercises \(74-77\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every line in the rectangular coordinate system has an equation that can be expressed in slope-intercept form.

Graph each linear equation in two variables. Find at least five solutions in your table of values for each equation. $$y=-\frac{5}{2} x-1$$

Will help you prepare for the material covered in the next section. From \((0,1),\) move 2 units down and 3 units to the right. What point do you obtain?

A new car worth 24,000 dollars is depreciating in value by 3000 dollars per year. The mathematical model $$y=-3000 x+24,000$$ describes the car's value, \(y,\) in dollars, after \(x\) years. a. Find the \(x\) -intercept. Describe what this means in terms of the car's value. b. Find the \(y\) -intercept. Describe what this means in terms of the car's value. c. Use the intercepts to graph the linear equation. Because \(x\) and \(y\) must be nonnegative (why?), limit your graph to quadrant I and its boundaries. d. Use your graph to estimate the car's value after five years.