Question 1

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph.
-$$2 x - 3 y = 9$$

Accepted Answer

To find the values of $x$ and $y$, we substitute the given points into the equation $2x - 3y = 9$.For the point $(x, 2)$, substitute $y = 2$:$$2x - 3(2) = 9$$$$2x - 6 = 9$$$$2x = 15$$$$x = \frac{15}{2}$$For the point $(8, y)$, substitute $x = 8$:$$2(8) - 3y = 9$$$$16 - 3y = 9$$$$-3y = -7$$$$y = \frac{7}{3}$$Therefore, the correct values are $x = \frac{15}{2}$ and $y = \frac{7}{3}$.

Question 2

Find a slope-intercept form equation for the line.
-Through $( 0,5 )$, with slope $\frac { 2 } { 3 }$

Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given the slope $\frac{2}{3}$ and passing through $(0,5)$, the y-intercept $b$ is 5. Thus, the equation is $y = \frac{2}{3}x + 5$.

Question 3

Solve the problem.
-Let C(x) = 900 + 30x be the cost to manufacture x items. Find the average cost per item to produce 20 items. Round to the nearest dollar.

Accepted Answer

The average cost per item for 20 items is calculated by dividing the total cost to manufacture 20 items by 20. The total cost for 20 items is C(20) = 900 + 30(20) = 900 + 600 = 1500. Therefore, the average cost per item is 1500 / 20 = $75.

Question 4

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( 1,4 )$, perpendicular to $x = 5$

Accepted Answer

The line $x = 5$ is a vertical line. A line perpendicular to a vertical line is a horizontal line. Horizontal lines have the equation $y = k$, where $k$ is the y-coordinate through which the line passes. Since the line passes through $(1,4)$, the equation of the line is $y = 4$.

Question 5

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( 9,4 )$, perpendicular to $6 x + 5 y = 34$

Accepted Answer

The slope of the line $6x + 5y = 34$ is $-\frac{6}{5}$. A line perpendicular to it will have a slope of $\frac{5}{6}$. Using the point-slope form with point $(9,4)$, the equation is $y - 4 = \frac{5}{6}(x - 9)$, which simplifies to $y = \frac{5}{6}x - \frac{7}{2}$.

Question 6

Solve the problem.
-Suppose y = mx + b is a mathematical model for actual time as a function of estimated time, where y represents actual time and x represents estimated time and m and b are constants. If m = 1.4 and b = -4.5, find y when x is
60 min.

Accepted Answer

The answer of Solve the problem.
-Suppose y = mx +...

Question 7

Find a slope-intercept form equation for the line.
-$$4 x - 11 y = 32$$

Accepted Answer

The answer of Find a slope-intercept form equation for the...

Question 8

Solve the problem.
-Suppose the sales of a particular brand of appliance satisfy the relationship $S ( x ) = 210 x + 4100$, where $S ( x )$ represents the number of sales in year $x$, with $x = 0$ corresponding to 1982 . Find the number of sales in 1996 .

Accepted Answer

To find the number of sales in 1996, calculate $x$ as 1996 - 1982 = 14. Substitute $x = 14$ into the equation: $S(14) = 210(14) + 4100 = 7040$.

Question 9

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( 3 , - 6 )$, perpendicular to $- 3 x + 2 y = - 21$

Accepted Answer

The slope of the given line is 3/2, so the slope of the perpendicular line is -2/3. The line passes through the point (3, -6), so the equation of the line in slope-intercept form is y = -2/3x - 4.

Question 10

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph.
-$$y = 3 x + 7$$

Accepted Answer

To find the value of x when y = 2, substitute y = 2 into the equation and solve for x: $2 = 3x + 7$, which simplifies to $x = -\frac{5}{3}$. To find the value of y when x = 8, substitute x = 8 into the equation: $y = 3(8) + 7$, which simplifies to $y = 31$. Therefore, the correct values are $x = -\frac{5}{3}$ and $y = 31$.

Question 11

Find a slope-intercept form equation for the line.
-Through the points $( 3,5 )$ and $( - 3,7 )$

Accepted Answer

The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(3,5)$ and $(-3,7)$, $m = \frac{7 - 5}{-3 - 3} = \frac{2}{-6} = -\frac{1}{3}$. To find the y-intercept $b$, use one of the points and the slope in the equation $y = mx + b$. Using point $(3,5)$, $5 = -\frac{1}{3}(3) + b$, solving for $b$ gives $b = 6$. Thus, the equation is $y = -\frac{1}{3}x + 6$.

Question 12

Find a slope-intercept form equation for the line.
-Through $( 0,3 )$, with slope $- \frac { 4 } { 9 }$

Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given the slope $- \frac { 4 } { 9 }$ and passing through $(0,3)$, the equation is $y = - \frac { 4 } { 9 } x + 3$.

Question 13

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph.
-$$y = - 0.5 x + 7$$

Accepted Answer

To find the value of $x$ when $y = 2$, substitute $y = 2$ into the equation and solve for $x$:$$2 = -0.5x + 7$$$$0.5x = 5$$$$x = 10$$To find the value of $y$ when $x = 8$, substitute $x = 8$ into the equation:$$y = -0.5(8) + 7$$$$y = -4 + 7$$$$y = 3$$Thus, $x = 10$ and $y = 3$, which corresponds to choice B.

Question 14

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( - 7 , - 5 )$, perpendicular to $6 x + 5 y = - 67$

Accepted Answer

The answer of Determine the equation of the line described....

Question 15

Solve the problem.
-Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $3500 in 1982 and $74,000 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).

Accepted Answer

The slope of the line is calculated as (74000 - 3500) / (1987 - 1982) = 14,100. The equation of the line is S(x) = 14,100x + 3500, where x = 0 represents 1982.

Question 16

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( - 3 , - 14 )$, parallel to $3 x + 8 y = - 65$

Accepted Answer

Lines that are parallel have the same slope. The given equation $3x + 8y = -65$ can be rewritten in slope-intercept form as $y = -\frac{3}{8}x - \frac{65}{8}$, indicating a slope of $-\frac{3}{8}$. To find the equation of a line parallel to this and passing through $(-3, -14)$, we use the slope $-\frac{3}{8}$ and the point $(-3, -14)$ in the point-slope form $y - y_1 = m(x - x_1)$, which simplifies to $y = -\frac{3}{8}x - \frac{121}{8}$ in slope-intercept form.

Question 17

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( - 7,11 )$ parallel to $4 x - 3 y = - 49$

Accepted Answer

Lines that are parallel have the same slope. The given equation $4x - 3y = -49$ can be rewritten in slope-intercept form as $y = \frac{4}{3}x + \frac{49}{3}$. The slope of this line is $\frac{4}{3}$, so the parallel line through $(-7, 11)$ will also have a slope of $\frac{4}{3}$. Using the point-slope form $y - y_1 = m(x - x_1)$ with $m = \frac{4}{3}$, $x_1 = -7$, and $y_1 = 11$, we get $y - 11 = \frac{4}{3}(x + 7)$. Simplifying this to slope-intercept form gives $y = \frac{4}{3}x + \frac{61}{3}$.

Question 18

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph.
-$$2 x + 3 y = 5$$

Accepted Answer

Substitute y = 2 into the equation to find x, and x = 8 to find y. Solving gives x = -1/2 and y = -11/3.

Question 19

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph.
-$$- 4 x - 3 y = 9$$

Accepted Answer

The answer of Find the value of x and the...

Question 20

Find a slope-intercept form equation for the line.
-Through $( 0,3 )$, with slope $\frac { 5 } { 4 }$

Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given a slope of $\frac{5}{4}$ and passing through $ (0,3) $, the equation is $y = \frac{5}{4}x + 3$, making option D correct.

Quiz 12: Prerequisites

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - $2 x - 3 y = 9$

Find a slope-intercept form equation for the line. -Through $( 0,5 )$ , with slope $\frac { 2 } { 3 }$

Solve the problem. -Let C(x) = 900 + 30x be the cost to manufacture x items. Find the average cost per item to produce 20 items. Round to the nearest dollar.

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( 1,4 )$ , perpendicular to $x = 5$

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( 9,4 )$ , perpendicular to $6 x + 5 y = 34$

Solve the problem. -Suppose y = mx + b is a mathematical model for actual time as a function of estimated time, where y represents actual time and x represents estimated time and m and b are constants. If m = 1.4 and b = -4.5, find y when x is 60 min.

Find a slope-intercept form equation for the line. - $4 x - 11 y = 32$

Solve the problem. -Suppose the sales of a particular brand of appliance satisfy the relationship $S ( x ) = 210 x + 4100$ , where $S ( x )$ represents the number of sales in year $x$ , with $x = 0$ corresponding to 1982 . Find the number of sales in 1996 .

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( 3 , - 6 )$ , perpendicular to $- 3 x + 2 y = - 21$

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - $y = 3 x + 7$

Find a slope-intercept form equation for the line. -Through the points $( 3,5 )$ and $( - 3,7 )$

Find a slope-intercept form equation for the line. -Through $( 0,3 )$ , with slope $- \frac { 4 } { 9 }$

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - $y = - 0.5 x + 7$

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( - 7 , - 5 )$ , perpendicular to $6 x + 5 y = - 67$

Solve the problem. -Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $3500 in 1982 and $74,000 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x) .

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( - 3 , - 14 )$ , parallel to $3 x + 8 y = - 65$

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( - 7,11 )$ parallel to $4 x - 3 y = - 49$

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - $2 x + 3 y = 5$

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - $- 4 x - 3 y = 9$

Find a slope-intercept form equation for the line. -Through $( 0,3 )$ , with slope $\frac { 5 } { 4 }$

Quiz 12: Prerequisites

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - 2x−3y=92 x - 3 y = 92x−3y=9

Find a slope-intercept form equation for the line. -Through (0,5) ( 0,5 ) (0,5) , with slope 23\frac { 2 } { 3 }32​

Solve the problem. -Let C(x) = 900 + 30x be the cost to manufacture x items. Find the average cost per item to produce 20 items. Round to the nearest dollar.

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (1,4) ( 1,4 ) (1,4) , perpendicular to x=5x = 5x=5

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (9,4) ( 9,4 ) (9,4) , perpendicular to 6x+5y=346 x + 5 y = 346x+5y=34

Solve the problem. -Suppose y = mx + b is a mathematical model for actual time as a function of estimated time, where y represents actual time and x represents estimated time and m and b are constants. If m = 1.4 and b = -4.5, find y when x is 60 min.

Find a slope-intercept form equation for the line. - 4x−11y=324 x - 11 y = 324x−11y=32

Solve the problem. -Suppose the sales of a particular brand of appliance satisfy the relationship S(x) =210x+4100S ( x ) = 210 x + 4100S(x) =210x+4100 , where S(x) S ( x ) S(x) represents the number of sales in year xxx , with x=0x = 0x=0 corresponding to 1982 . Find the number of sales in 1996 .

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (3,−6) ( 3 , - 6 ) (3,−6) , perpendicular to −3x+2y=−21- 3 x + 2 y = - 21−3x+2y=−21

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - y=3x+7y = 3 x + 7y=3x+7

Find a slope-intercept form equation for the line. -Through the points (3,5) ( 3,5 ) (3,5) and (−3,7) ( - 3,7 ) (−3,7)

Find a slope-intercept form equation for the line. -Through (0,3) ( 0,3 ) (0,3) , with slope −49- \frac { 4 } { 9 }−94​

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - y=−0.5x+7y = - 0.5 x + 7y=−0.5x+7

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (−7,−5) ( - 7 , - 5 ) (−7,−5) , perpendicular to 6x+5y=−676 x + 5 y = - 676x+5y=−67