Chapter 5

Without calculating, state whether the slope of the line through the points is positive, negative, zero, or undefined. (6,1),(3,1)

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. $$ -\frac{1}{2} \text { and } \frac{3}{2} $$

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(7,3), m=-2$$

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. $$ (6,2), m=\frac{1}{2} $$

Evaluate the expression when \(x=-3\) and \(y=6 .\) $$\frac{3 x}{x+y}$$

Write an equation in slope-intercept form of the line that passes through the points. $$ (-8,9),(10,-3) $$

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

Without calculating, state whether the slope of the line through the points is positive, negative, zero, or undefined. (5,2),(4,3)

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. \(-7\) and 2

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. $$ (-3,-1), m=4 $$

Write an equation in slope-intercept form of the line that passes through the points. $$ \left(\frac{1}{4}, 2\right),\left(-5, \frac{2}{3}\right) $$

Use the following information. In \(1991,\) the population of Kenosha, Wisconsin, was \(132,000 .\) Between 1991 and 1996 , the population of Kenosha increased by approximately 2000 people per year. Write an equation that models the population \(y\) of Kenosha in terms of \(x\) where \(x\) represents the number of years since 1991.

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(0,3), m=1 $$

Write an equation of the line that passes through the points. (2,5),(6,4)

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. $$ -3 \text { and }-\frac{7}{2} $$

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. $$ (5,-1), m=-1 $$

Write an equation in slope-intercept form of the line that passes through the points. $$ \left(\frac{1}{2},-\frac{1}{2}\right),\left(\frac{1}{9}, \frac{3}{9}\right) $$

Use the following information. In \(1991,\) the population of Kenosha, Wisconsin, was \(132,000 .\) Between 1991 and 1996 , the population of Kenosha increased by approximately 2000 people per year. Use the model to estimate the population of Kenosha in 2006 .

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

Write an equation of the line in slope-intercept form. The slope is \(2 ;\) the \(y\) -intercept is \(-5\)

Write an equation of the line that passes through the points. (1,4),(3,7)

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. $$ (-5,-5), m=-2 $$

You are designing a newspaper page with three photos. The page is \(13 \frac{1}{4}\) inches wide with 1 inch margins on both sides. You need to allow \(\frac{3}{4}\) inch between photographs. How wide should you make the photos if they are of equal size? Sketch a diagram of the newspaper page.

Write an equation in slope-intercept form of the line that passes through the points. $$ (-8.5,6.75),(3.33,-9.75) $$

Use the following information. At the start of your second year as a veterinary technician, you receive a raise of \(\$750.\) You expect to receive the same raise every year. Your total yearly salary after your first raise is \(\$ 18,000\) per year. Write an equation that models your total salary \(s\) in terms of the number of years \(n\) since you started as a technician.

Write an equation of the line that passes through the points. (3,7),(7,3)

Write an equation in standard form of the line that passes through the two points. $$(1,4),(5,7)$$

Write an equation of the line in slope-intercept form. The slope is \(\frac{1}{2} ;\) the \(y\) -intercept is \(-8\).

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. $$ (-1,1), m=-\frac{1}{8} $$

Which of the lines are perpendicular? Explain. $$ \text { line } p: y=\frac{1}{5} x+2 \quad \text { line } q: y=5 x-\frac{1}{2} \quad \text { line } r: y=-5 x+3 $$

Use the following information. At the start of your second year as a veterinary technician, you receive a raise of \(\$750.\) You expect to receive the same raise every year. Your total yearly salary after your first raise is \(\$ 18,000\) per year. Calculate your yearly salary after six years as a veterinary technician.

Write an equation of the line that passes through the points. (5,2),(4,3)

Write an equation in standard form of the line that passes through the two points. $$(-3,-3),(7,2)$$

Write an equation of the line in slope-intercept form. The slope is \(-4 ;\) the \(y\) -intercept is 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. $$ (4,-2), m=\frac{1}{4} $$

You are designing a newspaper page with three photos. The page is \(13 \frac{1}{4}\) inches wide with 1 inch margins on both sides. You need to allow \(\frac{3}{4}\) inch between photographs. How wide should you make the photos if they are of equal size? Solve the equation and answer the question.

Write an equation of a line through \((0,2)\) that is perpendicular to \(y=-4 x+6\)

Use the following information. You are moving to Houston, Texas, and are switching your cellular phone company. Your new peak air time rate in Houston is \(\$ .23\) per minute. Your bill also includes a monthly access charge. For 110 minutes of peak air time your bill is \(\$ 51.30\). Write an equation that models the cost \(C\) of your monthly bill in terms of the number of minutes \(m\) used. (All of your minutes are during peak air time.)

Write an equation of the line that passes through the points. (-3,1),(4,-2)

Write an equation in standard form of the line that passes through the two points. $$(-4,1),(2,-5)$$

Write an equation of the line in slope-intercept form. The slope is \(-2 ;\) the \(y\) -intercept is \(-6\)

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. $$ (-9,-6), m=-\frac{2}{3} $$

Match the description with the linear model \(y=10\) or the linear model \(y=10 x .\) Graph the model. You rent a sailboard for \(\$ 10\) per hour.

Write an equation of a line through \((4,5)\) that is perpendicular to \(y=\frac{1}{2} x+3\)

Use the following information. You are moving to Houston, Texas, and are switching your cellular phone company. Your new peak air time rate in Houston is \(\$ .23\) per minute. Your bill also includes a monthly access charge. For 110 minutes of peak air time your bill is \(\$ 51.30\). How much is your monthly bill for 60 minutes of peak air time?

Write an equation of the line that passes through the points. (-2,-3),(0,4)

Write an equation in standard form of the line that passes through the two points. $$(9,-2),(-3,2)$$

Write an equation in slope-intercept form of the line that passes through the point and has the given slope. $$ (6,5), m=2 $$

Match the description with the linear model \(y=10\) or the linear model \(y=10 x .\) Graph the model. You rent a life jacket for a flat fee of \(\$ 10 .\)

The cost of a taxi ride is an initial fee plus \(\$ 1.50\) for each mile. Your fare for 9 miles is \(\$ 15.50 .\) Write an equation that models the total cost \(y\) of a taxi ride in terms of the number of miles \(x\).