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## Texas Go Math Grade 8 Module 4 Quiz Answer Key

**Texas Go Math Grade 8 Module 4 Ready to Go On? Answer Key**

**4.1 Representing Linear Nonproportional Relationships**

Question 1.

Complete the table using the equation y = 3x + 2.

Answer:

In the given equation y = 3x + 2 include the given values of x.

x_{1} = -1 → y = 3 • (-1) + 2 = -3 + 2 → y = -1

x_{2} = 0 → y = 3 • 0 + 2 = 0 + 2 → y_{1} = 2

x_{3} = 1 → y = 3 • 1 + 2 = 3 + 2 → y_{1} = 5

x_{4} = 2 → y = 3 • 2 + 2 = 6 + 2 → y_{1} = 8

x_{5} = 3 → y = 3 • 3 + 2 = 9 + 2 → y_{1} = 11

Obtained values of y put in the tabla

**4.2 Determining Slope and y-intercept**

Question 2.

Find the slope and y-intercept of the line in the graph.

Answer:

The following equation for finding the slope and y-intercept is y = mx + b

The slope presents the ‘m’ in the equation, and the y-intercept represents b

The slope is calculated by:

m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

From the given graph, find two points that will help you calculate the slope.

I’ll take (0, 1) for (x_{1}, y_{1}) and (1, 4) for (x_{2}, y_{2}).

Thus: m = \(\frac{4-1}{1-0}\) = \(\frac{43}{1}\) = 3

To find the y-intercept, we need to include values of x and y from one of these two points, and include the obtained slope. So:

y = mx + b

1 = 3 . 0 + b

1 = 0 + b

b = 1

m = 3, b = 1

**4.3 Graphing Linear Nonproportional Relationships**

Question 3.

Graph the equation y = 2x – 3 using slope and y-intercept.

Answer:

y = 2x – 3

Slope = 2

y – intercept = -3

Plot the point that contains the y-intercept:

(0, -3)

The slope is m = \(\frac{2}{1}\)

Use the slope to find a second point.

From (0, -3) count $2$ unit up and $1$ unit right. The new point is (1, -1)

Draw a line through the points

**4.4 Proportional and Nonproportional Situations**

Question 4.

Does the table represent a proportional or a nonproportional linear relationship?

Answer:

To see if some linear relationship is proportional or nonproportional, we have to use ratio \(\frac{y}{x}\), which needs to be constant for proportionality.

From the given table, we have values for x and y, so just put them into the calculation.

\(\frac{y}{x}\) = \(\frac{4}{1}\) = 4

= \(\frac{8}{2}\) = 4

= \(\frac{12}{3}\) = 4

= \(\frac{16}{4}\) = 4

= \(\frac{20}{5}\) = 4

Thus, the obtained values are constant so this table represents a proportional relationship.

**4.5 Solving Systems of Linear Equations by Graphing**

Question 5.

A school band ordered hats for $3 and large T-shirts for $5. They bought 150 items in all for $590. Graph a system of equations to find how many hats and T-shirts the band ordered.

____________

Answer:

The graph represents the nonproportional relationship because the obtained b, ie y-intercept, is bigger than 0 (b /

= 0) and the line does not pass the origin. When the b = 0 and the line pass the origin, the linear relationship is proportional.

**Essential Question**

Question 6.

How can you identify a linear nonproportional relationship from a table, a graph, and an equation?

Answer:

The graph represents the nonproportional reLationship because the b, i.e. y-intercept from the given equation, is

bigger than 0 (b ≠ 0) and the line does not pass the origin. When the b = 0 and the line pass the origin, the linear relationship is proportional.

**Texas Go Math Grade 8 Module 4 Mixed Review Texas Test Prep Answer Key**

**Selected Response**

Question 1.

The table below represents which equation?

(A) y = -x – 10

(B) y = -6x

(C) y = 4x – 6

(D) y = -4x + 2

Answer:

(C) y = 4x – 6

Explanation:

The table is represented by Option C From the table, you can see that the y-intercept (when x = 0) is b = -6. Comparable to y = mx + b

y = 4x – 6

Question 2.

The graph of which equation is shown below?

(A) y = -2x + 3

(B) y = -2x + 1.5

(C) y = 2x + 3

(D) y = 2x + 1.5

Answer:

(A) y = -2x + 3

Explanation:

Option C is rejected

Since the graph is slanting downwards, the slope is negative.

The graph represents

y = -2x + 3

Question 3.

The table below represents a linear relationship.

What is the y-intercept?

(A) -4

(B) -2

(C) 2

(D) 3

Answer:

The y-intercept is -2.

Option B is the correct answer.

Question 4.

Which equation represents a nonproportional relationship?

(A) y = 3x + 0

(B) y = -3x

(C) y = 3x + 5

(D) y = \(\frac{1}{3}\)x

Answer:

(C) y = 3x + 5

Explanation:

Option C represents a non-proportional relationship

y = 3x + 5

For a non-proportional relationship, the equation is y = mx + b and b ≠ 0.

Question 5.

Which statement describes the solution of a system of linear equations for two lines with the same slope and the same y-intercept?

(A) one nonzero solution

(B) infinitely many solutions

(C) no solution

(D) solution of 0

Answer:

(B) infinitely many solutions

**Gridded Response**

Question 6.

The table shows a proportional relationship. What is the missing y-value?

Answer: