Chapter 5

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (5,-12), m=-11 $$

Write in standard form an equation of the line that passes through the given point and has the given slope. \((5,-8), m=\frac{1}{2}\)

Write in slope-intercept form the equation of the line that passes through the given points. $$ (1,4) \text { and }(-1,-4) $$

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (1,4), m=2 $$

Write in standard form an equation of the line that passes through the given point and has the given slope. \((7,3), m=-\frac{1}{3}\)

Write in slope-intercept form the equation of the line that passes through the given points. $$ (2,-3) \text { and }(-3,7) $$

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (-2,4), m=3 $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((4,0),(0,5)\)

Write in slope-intercept form the equation of the line that passes through the given points. $$ (2,2) \text { and }(-7,-7) $$

Use the following information. You are buying vegetables to make a vegetable tray for a party. You buy 10 dollars worth of cauliflower and broccoli. The cauliflower costs 2 dollars per pound and the broccoli costs 1.25 dollars per pound. Write an equation in standard form that represents the different amounts (in pounds) of cauliflower \(C\) and broccoli \(B\) that you could buy.

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (-5,-5), m=-2 $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((-3,0),(0,2)\)

Write in slope-intercept form the equation of the line that passes through the given points. $$ (6,-4) \text { and }(2,8) $$

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (6,2), m=\frac{1}{2} $$

Write in slope-intercept form the equation of the line passing through the given point and perpendicular to the given line. $$ (2,6), y=-\frac{1}{2} x+4 $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((0,0),(2,0)\)

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (-1,1), m=-\frac{1}{3} $$

Write in slope-intercept form the equation of the line passing through the given point and perpendicular to the given line. $$ (0,3), y=\frac{7}{8} x $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((0,1),(1,-1)\)

Write in point-slope form the equation of the line. Then rewrite the equation in slope-intercept form. $$ (4,-2), m=\frac{1}{4} $$

Write in slope-intercept form the equation of the line passing through the given point and perpendicular to the given line. $$ (0,0), y=-\frac{1}{4} x-7 $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((-4,0),(0,-5)\)

You and a friend have 30 dollars to spend at a health center. It costs 10 dollars an hour to use the racquetball court and 5 dollars an hour to use the tennis court. Which equation represents the number of hours you can spend on each court? Let \(x\) represent the number of hours on the racquetball court and \(y\) represent the number of hours on the tennis court. A. \(5 x+10 y=30\) B. \(10 x+5 y=30\) C. \(5 y=10 x-30\) D. \(y=5 x+6\)

Write in slope-intercept form the equation of the line that is parallel to the given line and passes through the given point. $$ y=2 x-11,(3,4) $$

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

Your basketball team scores 84 points with no 3 -point baskets. Each free throw \(x\) is worth 1 point. Each field goal \(y\) is worth 2 points. Which equation relates the number of free throws with the number of field goals? F. \(y=2 x+1\) G. \(x+y=84\) H. \(2 x+y=84\) J. \(x+2 y=84\)

Write in slope-intercept form the equation of the line that is parallel to the given line and passes through the given point. $$ y=-\frac{3}{5} x+6,(-2,7) $$

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

Evaluate the numerical expression. $$6-3 \cdot 2$$

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

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

Evaluate the numerical expression. $$12 \div 3-3 \cdot 1$$

Write in slope-intercept form the equation of the line that is parallel to the given line and passes through the given point. $$ y=7 x-1,(8,0) $$

Write in standard form an equation of the line that passes through the two points. Use integer coefficients. \((4,-7),(5,-1)\)

Evaluate the numerical expression. $$4^{2}-6 \cdot(4+7)$$

Write in slope-intercept form the equation of the line that is parallel to the given line and passes through the given point. $$ y=-9 x-3,(0,-5) $$

Convert the units. 5 days to hours

Write in slope-intercept form the equation of the line that is parallel to the given line and passes through the given point. $$ y=\frac{1}{2} x,(8,-10) $$

Complete the statement with always, sometimes, or never. A horizontal line is ____ perpendicular to a vertical line.

At sea level, the speed of sound in air is linearly related to the air temperature. If the temperature is \(35^{\circ} \mathrm{C},\) sound will travel at a rate of 352 meters per second. If the temperature is \(15^{\circ} \mathrm{C},\) sound will travel at a rate of 340 meters per second. Given the points \((35,352)\) and \((15,340),\) write in slope-intercept form the equation of the line that models this relationship.

Convert the units. 36 inches to feet

Complete the statement with always, sometimes, or never. The product of the slopes of two nonvertical perpendicular lines is ____ 1.

What is the equation of the line that passes through the points \((7,4)\) and \((-5,-2) ?\) A. \(y=\frac{1}{2} x-\frac{1}{2}\) B. \(y=-\frac{1}{2} x+\frac{1}{2}\) C. \(y=-\frac{1}{2} x-\frac{1}{2}\) D. \(y=\frac{1}{2} x+\frac{1}{2}\)

Convert the units. 12 years to months

Complete the statement with always, sometimes, or never. The line \(y=2 x+3\) is _____ perpendicular to a line with slope \(-2\)

Solve the equation. $$ 4 x-11=-31 $$

Write in slope-intercept form the equation of line that passes through the given points. \(m=0, b=7\)

At the end of the eighteenth century Benjamin Banneker was recommended by Thomas Jefferson to help lay out the new capital, Washington, D.C. As you can see in the map below, the city is laid out in a grid system of perpendicular streets. Assuming the \(x\) -axis is \(\mathrm{F}\) Street and the \(y\) -axis is 16 th Street, what is the equation of the line that passes through the point \((-4,1)\) and is perpendicular to 13 th Street \((x=3) ?\)

Using the point \((40,32.5)\) and the slope \(0.455,\) write the equation in point-slope form that models this situation. Then rewrite the equation in slope-intercept form.

Solve the equation. $$ 5 x-7+x=19 $$