Adam calculates his annual salary (base pay and commission), y, using the model y = 0.28x + 38,000, where x represents his total sales for the year.(5 points)

Question

1) What is the y-intercept? (Response area)

2) What does the y-intercept mean in context? (Response area)

3) What is the slope? (Response area)

4) What does the slope mean in context? (Response area)

5) If Adam made $45,000 total annual salary, how much was his total sales? (Response area)

responses
(0, 38,000)
2/8
the increase in salary per total sales
$25,000
$50,600
$7,000
(0, 0.28)
Adam's base salary
0.28

Answer 1

1. The y-intercept is (0, 38,000).

2. The y-intercept means that if Adam has zero total sales (x = 0), his annual salary (y) would be $38,000. This represents Adam's base salary, which he earns irrespective of his sales performance.

3. The slope is 0.28.

4. The slope means that for every dollar increase in total sales (x), Adam's annual salary (y) increases by $0.28. This indicates the increase in salary per dollar of total sales.

5. To find Adam's total sales when he made $45,000 total annual salary, we can set up the equation:

\[ 45,000 = 0.28x + 38,000 \]

Now, we solve for x:

1. Subtract 38,000 from both sides: \[ 45,000 - 38,000 = 0.28x \] \[ 7,000 = 0.28x \]

2. Divide both sides by 0.28: \[ x = \frac{7,000}{0.28} \] \[ x ≈ 25,000 \]

So, Adam's total sales were approximately $25,000.

Answer 2

Use the graph to answer the following questions:
the graph line starts at (0, 150) then goes up to (21, 475)

(6 points)
1) Is the graph increasing or decreasing?

2) Is the graph linear or non linear?

3) What is the slope?
responses
5/1
1/15
15/1
4) What does the slope mean in context?
responses
the cost is rising $15/linear foot
it costs $1 for 15 feet of fencing
5) What is the x-intercept?
responses
(-10, 0)
(150, 0)
6) What does the x-intercept mean in context?
responses
no meaning - you can't have negative linear feet
the starting cost is $150

Answer 3

1. The graph is increasing since the line goes upward from left to right.

2. The graph is linear because it forms a straight line with a constant slope.

3. To calculate the slope (m) using the two points (0, 150) and (21, 475), we use the formula for slope:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{475 - 150}{21 - 0} = \frac{325}{21} \approx 15.48 \]

Given the response options, the closest simplified form is 15/1 since this indicates an approximate cost per unit.

4. The slope means in context that the cost is rising $15 per linear foot. This indicates that for every additional linear foot of fencing, the cost increases by $15.

5. The x-intercept can be found by setting y = 0 and solving for x based on the equation of the line. To calculate the x-intercept, we start with the slope-intercept form of a line (y = mx + b). From our slope (15) and y-intercept (150):

\[ 0 = \frac{15}{1}x + 150 \]

Solving for x gives:

\[ 0 = 15x + 150 \ 15x = -150 \ x = -10 \]

Thus, the x-intercept is (-10, 0).

6. The x-intercept means in context that there is no meaning - you can't have negative linear feet. This indicates that negative lengths of fencing are not applicable in the real world.

Answer 4

Compare the functions:

Function A:

y=−3x+2

Function B:
x y
1 4
2 6
3 8
4 10
(1 point)
Responses

Function A is decreasing, while Function B is increasing AND Function B is steeper.
Function A is decreasing, while Function B is increasing AND Function B is steeper.

Function A is increasing, while Function B is decreasing AND Function B is steeper.
Function A is increasing, while Function B is decreasing AND Function B is steeper.

Function A is decreasing, while Function B is increasing AND Function A is steeper.
Function A is decreasing, while Function B is increasing AND Function A is steeper.

Function A is decreasing and Function B is also decreasing AND Function A is steeper.
Function A is decreasing and Function B is also decreasing AND Function A is steeper.
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Answer 5

Let's analyze both functions to determine their behavior and steepness.

Function A: The function \( y = -3x + 2 \) is a linear function with a slope of -3. Since the slope is negative, this means that Function A is decreasing.

Function B: To find the slope of Function B using the given points, we can take two points from the table and calculate the slope:

• Using the points (1, 4) and (2, 6):

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 4}{2 - 1} = \frac{2}{1} = 2 \]

Since the slope is positive, this means that Function B is increasing.

Now let's consider the steepness:

• Function A has a steeper slope of -3 (in the absolute sense) compared to Function B's slope of 2. Since steepness refers to the magnitude of the slope regardless of the direction, we look at absolute values:
  • |Slope of Function A| = 3
  • |Slope of Function B| = 2
• Therefore, Function A is steeper because |3| > |2|.

Final Conclusion:

• Function A is decreasing, while Function B is increasing, AND Function A is steeper.

The correct response is: Function A is decreasing, while Function B is increasing AND Function A is steeper.

Answer 6

The equation of a line is given by Ax + By = C. Solve for y.(1 point)
Responses

y=C/B−Ax/B
y is equal to cap c over cap b minus cap A x over cap b

y=C−Ax
y is equal to cap c minus cap A x

y=B(C−Ax)
y is equal to cap b times open paren cap c minus cap A x close paren

y=C−Ax/B

Answer 7

To solve the equation of a line given by \( Ax + By = C \) for \( y \), we follow these steps:

1. Start with the original equation: \[ Ax + By = C \]

2. Subtract \( Ax \) from both sides: \[ By = C - Ax \]

3. Finally, divide both sides by \( B \): \[ y = \frac{C - Ax}{B} \]

This expression can also be written as: \[ y = \frac{C}{B} - \frac{A}{B}x \]

From the provided responses:

• y = C - Ax / B is the most accurate representation of the final result when properly formatted.

Thus, the correct response is: y = C - Ax/B.

Answer 8

Which of the following represents a linear function with the same slope as the table below? *Select 2 that apply!

(2 points)
Responses
x f (x)
-4 14
-2 8
3 -7
5 -13

James increases his muscle mass by 3 kg per day.
James increases his muscle mass by 3 kg per day.

6x−2y=12
6 x minus 2 y is equal to 12

Cynthia has $200 in her savings account and spends $3 per day on coffee.
Cynthia has $200 in her savings account and spends $3 per day on coffee.
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Answer 9

To determine which of the given options represents a linear function with the same slope as the data shown in the table, we need to first find the slope of the relationship given in the table.

Provided table values:

• \( x = -4, f(x) = 14 \)
• \( x = -2, f(x) = 8 \)
• \( x = 3, f(x) = -7 \)
• \( x = 5, f(x) = -13 \)

Calculate the slope (m):

We can use two points from the table to calculate the slope using the formula: \[ m = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \]

Let's take the first two points \((-4, 14)\) and \((-2, 8)\): \[ m = \frac{8 - 14}{-2 - (-4)} = \frac{-6}{2} = -3 \]

This means the slope of the linear function represented by the values in the table is -3.

Now, let's check the options:

1. James increases his muscle mass by 3 kg per day.

   • This represents a linear relationship with a slope of 3 (not -3).

2. 6x - 2y = 12

   • To find the slope of this equation, convert it to slope-intercept form (y = mx + b): \[ 6x - 2y = 12 \ -2y = -6x + 12 \ y = 3x - 6 \] The slope here is 3 (not -3).

3. Cynthia has $200 in her savings account and spends $3 per day on coffee.

   • This represents a linear relationship with a slope of -3 (because she is spending money, decreasing her savings).

Conclusion:

The two choices that represent a linear function with a slope of -3 are:

• Cynthia has $200 in her savings account and spends $3 per day on coffee.
• None of the other choices match the slope of -3.

So the correct answer is:

• Cynthia has $200 in her savings account and spends $3 per day on coffee.

Answer 10

The equation of Line 1: 2x−4y=16


The equation of Line 2: y=−34x−3


The equation of Line 3: y−5=−2(x+1)


Which statement is true?

(2 points)
Responses

Line 1 has the steepest slope.
Line 1 has the steepest slope.

Line 3 has the least steep slope.
Line 3 has the least steep slope.

Line 1 has the biggest y-intercept.
Line 1 has the biggest y-intercept.

Line 2 has the biggest y-intercept.
Line 2 has the biggest y-intercept.

Line 3 has a decreasing graph.
Line 3 has a decreasing graph.

Line 2 has an increasing graph.

Answer 11

To determine which statement is true among the given options, we need to find the slopes and y-intercepts of each line.

Line 1: \( 2x - 4y = 16 \)

1. Convert to slope-intercept form \(y = mx + b\):

\[ -4y = -2x + 16 \ y = \frac{1}{2}x - 4 \]

• Slope (m): \(\frac{1}{2}\)
• Y-intercept (b): \(-4\)

Line 2: \( y = -\frac{3}{4}x - 3 \)

This line is already in slope-intercept form.

• Slope (m): \(-\frac{3}{4}\)
• Y-intercept (b): \(-3\)

Line 3: \( y - 5 = -2(x + 1) \)

1. Convert to slope-intercept form:

\[ y - 5 = -2x - 2 \ y = -2x + 3 \]

• Slope (m): \(-2\)
• Y-intercept (b): \(3\)

Summary of Slopes and Y-intercepts:

• Line 1: Slope = \(\frac{1}{2}\), Y-intercept = \(-4\)
• Line 2: Slope = \(-\frac{3}{4}\), Y-intercept = \(-3\)
• Line 3: Slope = \(-2\), Y-intercept = \(3\)

Now, let's evaluate the statements:

1. Line 1 has the steepest slope.

   • The slopes: \(\frac{1}{2}\) (Line 1), \(-\frac{3}{4}\) (Line 2), and \(-2\) (Line 3). The steepest (most negative) slope is from Line 3. So, this statement is false.

2. Line 3 has the least steep slope.

   • Line 3 has a slope of \(-2\), which is the steepest. Thus, this statement is false.

3. Line 1 has the biggest y-intercept.

   • The y-intercepts are \(-4\) (Line 1), \(-3\) (Line 2), and \(3\) (Line 3). Line 3 has the biggest y-intercept. So, this statement is false.

4. Line 2 has the biggest y-intercept.

   • This is also false as Line 3 has the biggest y-intercept.

5. Line 3 has a decreasing graph.

   • Line 3 has a negative slope (\(-2\)), so it is decreasing. This statement is true.

6. Line 2 has an increasing graph.

   • Line 2 has a negative slope (\(-\frac{3}{4}\)), so it is decreasing. Thus, this statement is false.

Conclusion:

The true statement is: Line 3 has a decreasing graph.