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Katarina wrote the standard form of a linear equation as 4x – y = 8. Sofiya told her that the equation was not yet in standard form and gave her the right advice for how to fix it. What advice did Sofiya give to Katarina?

Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24.

Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 12.

Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 8.

Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x – y = 4.

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Will’s meal of grilled chicken strips and carrots contained a total of 333 calories. The bag of grilled chicken strips contained x servings of 110 calories each. The bag of carrots contained y servings of 29 calories each. Which equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten?

110y = –29x + 333

29x + 110y = 333

29y = –110x + 333

110x + 29y = 333

A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. Which equation represents the shipping cost as a function of x, the weight in pounds?

f(x) = 2.25x + 5

f(x) = 5x + 2.25

f(x) = 2.25x − 5

f(x) = 5x − 2.25

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2), and (1, negative 1). Everything to the right of the line is shaded.

(0, 2)

(2, 0)

(1, −2)

(−2, 1)

At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

x + y < 12

x + y > 12

x + y ≤ 12

x + y ≥ 12

The graph shows the amount of money Miguel earns after working x hours.

hours per dollar

hours per dollar

3 dollars per hour

13 dollars per hour

Which is the graph of the equation ?

Option

A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).

–3x + 2 = y

–x + 2 = y

x – 3 = y

2x – 3 = y

Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?

It is linear because the graph decreases over time.

It is linear because there is both an independent and a dependent variable.

It is nonlinear because linear functions are increasing functions.

It is nonlinear because linear functions increase or decrease at the same rate.

A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

Option

On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1.3) and (3, negative 0.3). Everything below and to the right of the line is shaded.

y ≤ x – 1.3

y ≤ x –

y ≥ x –

y ≥ x – 1.3

Which equation represents a line that passes through (2, –) and has a slope of 3?

y – 2 = 3(x + )

y – 3 = 2(x + )

y + = 3(x – 2)

y + = 2(x – 3)

The table shows the profit from a school book fair based on the number of books sold.

$0.50 per book

$0.67 per book

$1.07 per book

$1.50 per book

Which description of the graph of the linear inequality y ≥ 7x – 4 is correct?

The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.

The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.

What is the y-intercept of the function f(x)=4 – 5x?

–5

–4

Which shows the graph of x – 4y =–4?

A coordinate plane with a line passing through (0, negative 4) and (1, 0).

A coordinate plane with a line passing through (negative 4, negative 2), (0, negative 1) and (4, 0).

A coordinate plane with a line passing through (negative 2, negative 4), (negative 1, 0) and (0, 4).

A coordinate plane with a line passing through (negative 4, 0) and (0, 1).

Alejandra correctly wrote the equation y – 3 = (x – 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

y – 6 = 2(x – 10)

y – 2 = (x – 10)

y – 3 = (x – 2)

y – 3 = 2(x – 10)

A coordinate plane with a line passing through (0, negative 5) and (3, 0).

3x + y = –5

x + 3y = –5

3x – 5y = –15

5x – 3y = 15

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?

inch up per foot across

2 inches up per foot across

3 inches up per foot across

A coordinate plane from negative 8 to 8 along the x-axis and from negative 7 to 7 along the y-axis.

1. Plot the point (2, 4).2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

1. Plot the point (2, 4).2. From that point, count left 1 unit and down 3 units and plot a second point. 3. Draw a line through the two points.

1. Plot the point (–2,4).2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

1. Plot the point (–2,4).2. From that point, count left 1 unit and down 3 units and plot a second point. 3. Draw a line through the two points.

A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded.

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above the line is shaded.

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded.

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the right of the line is shaded.

A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?

12 ≤ x + y

12 ≥ x + y

12 ≤ 2x + 3y

12 ≥ 2x + 3y

What is the slope of the line represented by the equation f(t)=2t−6?

The slope is 2 and the y-intercept is −6.

The slope is −6 and the y-intercept is 2.

The slope is 2 and the y-intercept is 6.

The slope is 6 and the y-intercept is 2.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.

y < x + 3

y > x + 3

y < x + 3

Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?

x + y < 8

x + y > 8

x + y ≤ 8

x + y ≥ 8

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