Slope and Intercept Insights: Linear Systems Quiz

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 20 + 0.20m; Slope = 0.20, representing the flat fee.

• C = 20 + 0.15m; Slope = 0.15, representing the cost per mile.

• C = 20 + 0.10m; Slope = 0.10, representing the total cost.

• C = 15 + 0.15m; Slope = 0.15, representing the base charge.

Tags

CCSS.HSF.LE.B.5

Two friends are jogging on parallel paths. One path is represented by the equation y = 2x + 3 and the other by y = 2x - 1. Are these paths parallel or perpendicular? Explain your reasoning.

• The paths have different slopes.

• The paths are parallel.

• The paths intersect at a point.

• The paths are perpendicular.

A local bakery sells cupcakes for $3 each and cookies for $2 each. If the total revenue from selling x cupcakes and y cookies is $60, write the equation representing this situation. What is the y-intercept and what does it signify?

• The equation is 3x + 2y = 30; the y-intercept is 15, representing the number of cupcakes sold.

• The equation is 4x + y = 60; the y-intercept is 60, showing the total number of items sold.

• The equation is 2x + 3y = 60; the y-intercept is 20, indicating the total revenue from cookies.

• The equation is 3x + 2y = 60; the y-intercept is 30, signifying the maximum number of cookies that can be sold for $60 if no cupcakes are sold.

Tags

CCSS.HSF-IF.C.7A

A line has a slope of -3 and passes through the point (2, 5). Write the equation of the line in slope-intercept form. What does the y-intercept represent in this scenario?

• y = -3x + 11; The y-intercept (11) represents the value of y when x = 0, indicating the point where the line crosses the y-axis.

• y = -3x + 5; The y-intercept (5) represents the slope of the line.

• y = 3x + 11; The y-intercept (11) shows the point where the line crosses the x-axis.

• y = -3x + 2; The y-intercept (2) indicates the maximum value of y.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Two lines are represented by the equations y = 1/2x + 4 and y = -2x + 1. Are these lines parallel, perpendicular, or neither? Justify your answer using their slopes.

• coincident

• parallel

• intersecting

• perpendicular

Tags

CCSS.8.EE.C.8B

A taxi charges a base fare of $2.50 and $0.50 for each mile driven. Write the equation for the total fare (F) in terms of miles driven (m). What does the slope indicate about the cost per mile?

• F = 2.50 + 1.00m; the slope indicates the cost per mile is $1.00.

• F = 2.50 + 0.50m; the slope indicates the cost per mile is $0.50.

• F = 2.50 + 0.25m; the slope indicates the cost per mile is $0.25.

• F = 2.50 - 0.50m; the slope indicates the cost per mile is $0.50.

Tags

CCSS.HSF.LE.B.5

A store sells notebooks for $1.50 each and pens for $0.75 each. If a student buys a total of 10 items for $9, write the system of equations that represents this situation. What do the intercepts represent?

• x + y = 10; 1.5x + 0.75y = 9

• x + y = 15; 1.5x + 0.75y = 12

• x + y = 10; 1.5x + 0.5y = 9

• x + y = 8; 1.5x + 0.75y = 10

Tags

CCSS.8.EE.C.8C

A line passes through the points (1, 2) and (3, 6). Calculate the slope and write the equation of the line. What does the slope tell you about the relationship between the x and y values?

• The slope is 0 and the equation of the line is y = 2.

• The slope is 3 and the equation of the line is y = 3x - 1.

• The slope is 1 and the equation of the line is y = x + 1.

• The slope is 2 and the equation of the line is y = 2x.

Tags

CCSS.8.EE.B.5