Unit 2 Exam In Class review

Write and solve the equation

modeled below.

Answer explanation

1. We're solving the equation 3x + 4 = -2x + 1 to find 'x.'

   1. 1. Add '3x' to both sides to move all the 'x' terms to one side, which gives us 4 = x + 1.

   2. 2. Subtract '-1' from both sides to get 3 = x

      3. Rewrite the answer a 'x=3".

Solve the following equation with

variables on both sides.

Answer explanation

1. Subtract 8x from both sides to get 13 = 6x + 1.

2. Then, subtract 1 from both sides to get 12 = 6x.

3. Finally, divide by 6 to find x = 2.

So, the answer is x = 2.

Marshall is a software engineer with a starting salary of $36,000, and each year he receives a $4,000 raise.

Jim, a product manager, earns a salary of $51,000, and each year he receives a $1,500 raise.

David, a new intern, is curious to know how many years it will take before Marshall and Jim earn the same salary?

Answer explanation

Marshall earns $36,000 and gets a $4,000 raise each year. Jim earns $51,000 and gets a $1,500 raise each year. To find when they earn the same, we set up an equation:

36,000 + 4,000x = 51,000 + 1,500x

1. 1. Solve for x (the number of years it takes):

36,000 - 51,000 = (1,500x - 4,000x) -15,000 = -2,500x

2. 2. Divide both sides by -2,500:

x = 6

So, it will take 6 years for Marshall and Jim to earn the same salary.

What is the slope of the equation?

Answer explanation

In the equation y = 6x, the number 6 represents the slope of the line.

It tells us that for every 1 unit increase in x, the y-value goes up by 6 units.

So, 6 is the slope of the equation. (Remember, Rise/Run!)

Graph y = 1/2x +3

Answer explanation

To graph the equation y = (1/2)x + 3:

1. Start at the point (0, 3).

2. Move up 1 unit and to the right 2 units to plot the point (2, 4).

3. Move down 1 unit and to the left 2 units to plot the point (-2, 2).

4. Connect these points with a straight line.

Your graph will be a diagonal line that passes through these points.

Graph y = -1/2x + 7

Answer explanation

To graph the equation y = -1/2x + 7:

1. Start at the point (0, 7).

2. Move down 1 unit and to the right 2 units to plot the point (2, 6).

3. Move up 1 unit and to the left 2 units to plot the point (-2, 8).

4. Connect these points with a straight line.

Your graph will be a diagonal line that passes through these points.

Aiden took his car to a repair company that charges a $15 fee for an evaluation plus an hourly rate for any services required. What is the hourly charge for services?

Answer explanation

The hourly charge for services is $75 per hour.

This is determined by subtracting the $15 evaluation fee from the total cost for different service durations (2 hours, 4 hours, 6 hours),

Which resulted in the same hourly rate of $75 per hour.

What are the 4 types of slopes?

• Zero

• 
• Negative

• 
• Positive

• 
• Undefined

• 

Answer explanation

1. Positive Slope: Line goes uphill (rises from left to right).

2. Negative Slope: Line goes downhill (falls from left to right).

3. Zero Slope: Line is perfectly horizontal (no rise or fall).

4. Undefined Slope: Line is perfectly vertical (no left or right movement).

These describe the direction and steepness of lines on a graph.

Kacie bought 5 breakfast wraps and 2 bottles of juice for $26. At the same

shop, Adam bought 3 breakfast wraps and 3 bottles of juice for $21. How much

does one breakfast wrap cost? How much does one bottle of juice cost?

• One breakfast wrap costs $2.50, and one bottle of juice costs $4.50

• One breakfast wrap costs $2.00, and one bottle of juice costs $4.00

• One breakfast wrap costs $4.00, and one bottle of juice costs $3.00

• One breakfast wrap costs $4.50, and one bottle of juice costs $2.50

Answer explanation

Kacie bought 5 breakfast wraps and 2 bottles of juice for $26, and Adam bought 3 breakfast wraps and 3 bottles of juice for $21.

From the information, we can determine that one bottle of juice costs $3 (since 2 bottles cost $6, and the total was $26).

To find the cost of one breakfast wrap, we know that a combination of one breakfast wrap and one bottle of juice costs $7 (because 3 breakfast wraps and 3 bottles of juice cost $21).

So, one breakfast wrap costs $4 (since $7 - $3 = $4).

Graph the solution to this system equation.