Question

Question 1-

Which equation represents the table?
A. y=1/2x+5
B. y=-1/2x+3
C. y=2x-3
D. y=-4x+2

Question 2-
Which of the following sets of ordered pairs represents a function?
A. {(−6, −5), (−4, −3), (-2, 0), (-2, 2), (0,4)}
B. {(−5, −5), (−5, −4), (−5, −3), (-5, -2), (-5, 0)}
C. {(-4, −5), (-3, 0), (−2, −4), (0, -3), (2, -2)
D. {(-6, -3), (-6, -2), (-5, -3), (-3, -3), (0, 0)}

Question 3-
Which of the following equations represents a linear function?
A. x=-2
B. y=5x-6
C. y=-1/5x²
D. -3x+2=4

Question 4-
The table represents a linear relationship.
x -2 0 4
y 4 3 1
Which equation represents the table?
A. y=1/2x+5
B. y=-1/2x+3
C. y=2x-3
D. y=-4x+2

Answer 1

Question 2: C. {(-4, −5), (-3, 0), (−2, −4), (0, -3), (2, -2)}.
Question 3: B. y = 5x - 6.
Question 4: B. y = -1/2x + 3.

Explanation:

Question 2: In a function, each input (x-value) corresponds to exactly one output (y-value). In set C, each x-value is paired with a unique y-value, satisfying the definition of a function.

Question 3: As explained earlier, a linear function has a constant rate of change, and its equation is in the form y = mx + b, where m is the slope and b is the y-intercept. Option B represents this form, indicating a linear function.

Question 4: To determine the equation, we need to find the slope (rate of change) and the y-intercept. By examining the table, we can see that the slope is -1/2 (y decreases by 1 when x increases by 2), and the y-intercept is 3 (the y-value when x = 0). Therefore, the equation y = -1/2x + 3 represents the given table's linear relationship.

Answer 2

=Question 1-

To determine which equation represents the table, we can compare the given equations to the values in the table. Plugging in the x-values from the table into each equation, we can check if the resulting y-values match the corresponding values in the table.

A. y = 1/2x + 5

For x = -2, y = 1/2(-2) + 5 = 4. This matches the value in the table.

For x = 0, y = 1/2(0) + 5 = 5. This does not match the value in the table.

For x = 4, y = 1/2(4) + 5 = 7. This does not match the value in the table.

B. y = -1/2x + 3

For x = -2, y = -1/2(-2) + 3 = 4. This matches the value in the table.

For x = 0, y = -1/2(0) + 3 = 3. This matches the value in the table.

For x = 4, y = -1/2(4) + 3 = 1. This matches the value in the table.

C. y = 2x - 3

For x = -2, y = 2(-2) - 3 = -7. This does not match the value in the table.

For x = 0, y = 2(0) - 3 = -3. This does not match the value in the table.

For x = 4, y = 2(4) - 3 = 5. This does not match the value in the table.

D. y = -4x + 2

For x = -2, y = -4(-2) + 2 = 10. This does not match the value in the table.

For x = 0, y = -4(0) + 2 = 2. This matches the value in the table.

For x = 4, y = -4(4) + 2 = -14. This does not match the value in the table.

Based on the comparisons, the equation that represents the table is B. y = -1/2x + 3.

Question 2-

To determine which set of ordered pairs represents a function, we need to check if there are any repeated x-values in the set. A function can only have one unique y-value for each x-value.

A. {(−6, −5), (−4, −3), (-2, 0), (-2, 2), (0,4)}

There are repeated x-values (-2) in this set, so it does not represent a function.

B. {(−5, −5), (−5, −4), (−5, −3), (−5, −2), (−5, 0)}

There are repeated x-values (-5) in this set, so it does not represent a function.

C. {(-4, −5), (-3, 0), (−2, −4), (0, -3), (2, -2)}

There are no repeated x-values in this set, so it represents a function.

D. {(-6, -3), (-6, -2), (-5, -3), (-3, -3), (0, 0)}

There are repeated x-values (-6) in this set, so it does not represent a function.

Therefore, the set of ordered pairs that represents a function is C. {(-4, −5), (-3, 0), (−2, −4), (0, -3), (2, -2)}.

Question 3-

To determine which equation represents a linear function, we need to look for equations that have a variable (x or y) raised to the power of 1 and do not have any other variables raised to a power.

A. x = -2

This equation represents a vertical line, not a linear function.

B. y = 5x - 6

This equation represents a linear function since it has the variable x raised to the power of 1 and no other variables raised to a power.

C. y = -1/5x²

This equation represents a quadratic function since it has the variable x raised to the power of 2.

D. -3x + 2 = 4

This equation represents a linear function since it has the variable x raised to the power of 1 and no other variables raised to a power.

Therefore, the equation that represents a linear function is B. y = 5x - 6.

Question 4-

To determine which equation represents the table, we can again compare the given equations to the values in the table.

A. y = 1/2x + 5

For x = -2, y = 1/2(-2) + 5 = 4. This matches the value in the table.

For x = 0, y = 1/2(0) + 5 = 5. This matches the value in the table.

For x = 4, y = 1/2(4) + 5 = 7. This does not match the value in the table.

B. y = -1/2x + 3

For x = -2, y = -1/2(-2) + 3 = 4. This matches the value in the table.

For x = 0, y = -1/2(0) + 3 = 3. This matches the value in the table.

For x = 4, y = -1/2(4) + 3 = 1. This matches the value in the table.

C. y = 2x - 3

For x = -2, y = 2(-2) - 3 = -7. This does not match the value in the table.

For x = 0, y = 2(0) - 3 = -3. This matches the value in the table.

For x = 4, y = 2(4) - 3 = 5. This does not match the value in the table.

D. y = -4x + 2

For x = -2, y = -4(-2) + 2 = 10. This does not match the value in the table.

For x = 0, y = -4(0) + 2 = 2. This matches the value in the table.

For x = 4, y = -4(4) + 2 = -14. This does not match the value in the table.

Based on the comparisons, the equation that represents the table is B. y = -1/2x + 3.