Chapter 5

Write a linear equation to model the situation. Use unit analysis to check your model. You have walked 5 miles on a hiking trail. You continue to walk at the rate of 2 miles per hour for 6 hours.

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=2 x+2,(3,2)$$

Will choosing the two points that are the farthest apart always give you the closest line? Explain why or why not. If not, sketch a counterexample.

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(-8,3), m=2$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (-8,-2), m=2 $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (-5,2),(6,1) $$

You are traveling home in a bus whose speed is 50 miles per hour. At noon you are 200 miles from home. Write an equation that models your distance \(y\) from home in terms of \(t,\) the number of hours since noon. Why does the line given by this equation have a negative slope?

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=x+4,(-2,0)$$

Explain how to choose a good pair of points to find a line that is probably close to the best-fitting line.

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(-2,7), m=-4$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (-4,3), m=-6 $$

You are designing a calendar as a fund-raising project for your Biology Club. The cost of printing is \(\$ 500\), plus S2.50 per calendar. (Graph cannot copy) Write an equation to model the total cost \(C\) of printing \(x\) calendars.

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (-6,2),(-4,11) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=-2 x+3,(4,4)$$

Decide whether the line is horizontal or vertical. Then graph the line. \(y=-2\)

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(-1,4), m=-3$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (-3,4), m=6 $$

You are designing a calendar as a fund-raising project for your Biology Club. The cost of printing is \(\$ 500\), plus S2.50 per calendar. (Graph cannot copy) You sell each calendar for \(\$ 5.00 .\) Write an equation to model the total income \(T\) for selling \(x\) calendars.

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (-1,10),(12,-4) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=-3 x+1,(4,2)$$

Decide whether the line is horizontal or vertical. Then graph the line. \(y=3\)

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(-6,-7), m=-1$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (12,2), m=-7 $$

Write an equation in slope-intercept form of the line that passes through the points. $$ (-6,-5),(1,4) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=\frac{2}{3} x-2,(2,1)$$

Decide whether the line is horizontal or vertical. Then graph the line. \(x=4\)

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(3,-2), m=5$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (8,-1), m=0 $$

Write an equation in slope-intercept form of the line that passes through the points. $$ (2,3),(4,3) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=-\frac{1}{3} x-1,(4,1)$$

Decide whether the line is horizontal or vertical. Then graph the line. \(x=-5\)

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. \(-7\) and 3

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(10,6), m=7$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (5,-12), m=-11 $$

Use the following information. The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2025 Choose the linear model that predicts the population \(P\) of Florida (in millions) in terms of \(t,\) the number of years since 2010 . A) \(P=17.4 t+0.22\) (B) \(P=-0.22 t+17.4\) (c) \(P=0.22 t+17.4\) (D) \(P=-17.4 t+0.22\)

Write an equation in slope-intercept form of the line that passes through the points. $$ (5,-10),(12,-7) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=-4 x-2,(5,3)$$

Without calculating, state whether the slope of the line through the points is positive, negative, zero, or undefined. (1,4),(3,5)

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. \(-2\) and \(-1\)

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(2,9), m=-7$$

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. $$ (1,4), m=2 $$

Write an equation in slope-intercept form of the line that passes through the points. $$ (14,-3),(-6,9) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=6 x+9,(5,-3)$$

Without calculating, state whether the slope of the line through the points is positive, negative, zero, or undefined. (2,5),(4,1)

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. 12 and \(-12\)

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(5,-8), m=10$$

Write the point-slope form of the equation of the line that passes through the point and has the given slope. Then rewrite the equation in slope-intercept form. $$ (-2,4), m=3 $$

In January, your ceramics class begins with 12 students. In every month after January, three new students join and one student drops out. a. Write a linear equation to model the situation. b. Graph the model. c. Predict the size of your ceramics class in May and June.

Write an equation in slope-intercept form of the line that passes through the points. $$ (-7,9),(-3,8) $$

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=-9 x-8,(7,-2)$$