Question 1

Concept Problem

What does a point on the graph of a linear function represent?

Accepted Answer

A pair of input and output values that satisfy the function

Answer

The slope of the function

Answer

A solution to an equation only

Answer

The y-intercept of the function

Question 2

Concept Problem

Which equation is written in slope-intercept form?

Accepted Answer

Answer

<math>y-2=3\left(x-4\right)</math>

Answer

Answer

Question 3

Concept Problem

Which of the following represents the standard form of the equation with x-intercept 4 and y-intercept -3?

Accepted Answer

Answer

Answer

Answer

Question 4

Concept Problem

What is the equation of the line in point-slope form that passes through the point (3, -2) with a slope of 4?

Accepted Answer

<math>y+2=4\left(x-3\right)</math>

Answer

<math>y+2=4\left(x+3\right)</math>

Answer

<math>y-2=4\left(x+3\right)</math>

Answer

<math>y-2=4\left(x-3\right)</math>

Question 5

Concept Problem

What is the y-value of the point (2, y) on the line given by the equation $y-1=3\left(x-2\right)$ ?

Accepted Answer

1

Answer

7

Answer

2

Answer

4

Question 6

Concept Problem

If a line in the coordinate plane passes through the points (2, 3)

and (6, 11), what is the slope of the line?

Accepted Answer

2

Answer

1

Answer

4

Answer

0.5

Question 7

Concept Problem

Which of the following correctly describes the slope of a vertical line?

Accepted Answer

Undefined

Answer

Zero

Answer

Negative

Answer

Positive

Question 8

Concept Problem

Which of the following pairs of linear equations are parallel?

Accepted Answer

$y=4x-9$ and $y=2x-3$

Answer

$y=4x-9$ and $y=2x-3$

Answer

$y=4x-9$ and $y=2x-3$

Answer

$y=4x-9$ and $y=2x-3$

Question 9

Concept Problem

Given the equation of a line in point-slope form

y+4=-3(x-2)

, what is the y-intercept of this line?

Accepted Answer

-10

Answer

4

Answer

8

Answer

2

Question 10

Concept Problem

A youth club is organizing a camping trip. The initial number of boys signed up is 40, and each week, 2 more boys join the trip. How long will it take for there to be 100 boys signed up?

Accepted Answer

30 weeks

Answer

40 weeks

Answer

20 weeks

Answer

25 weeks

Question 11

Logic Problem

Passage

To find the slope through $\left(-2,5\right)$ and $\left(4,-1\right)$ , a student writes: $m=\frac{-1-5}{-2-4}=\frac{-6}{-6}=1$ .

Question

What is the primary flaw in the student's computation?

Accepted Answer

The student subtracted y-values and x-values using inconsistent point order.

Answer

The student incorrectly simplified a negative fraction.

Answer

The student should have converted the points into intercept form first.

Answer

The student should have added the coordinates instead of subtracting.

Question 12

Logic Problem

Passage

To find the x-intercept of $y=2x-6$ , a student sets

x=0

, obtains

y=-6

, and concludes the x-intercept is −6.

Question

What is the error in this approach?

Accepted Answer

The student should set $y=0$ to find the x-intercept.

Answer

The student should set $y=0$ to find the x-intercept.

Answer

Intercepts cannot be found algebraically.

Answer

The student should set

y=4x-9

to find the x-intercept.

Question 13

Logic Problem

Passage

A table shows:

x: 2, 4, 6

y: 10, 4, −2

A student says, “The slope is 3 because y changes by 6 each time.”

Question

What is the most accurate critique?

Accepted Answer

The student ignored that the change in y is negative, not positive.

Answer

The student should use only the first two points.

Answer

The student used the intercept instead of slope.

Answer

Tables cannot represent linear functions.

Question 14

Logic Problem

Passage

Given $y=\frac{2}{3}x-4$ , a student states, "The slope is $\frac{3}{2}$ because you flip the fraction."

Question

What is wrong with this reasoning?

Accepted Answer

The student incorrectly took the reciprocal of the slope.

Answer

The student confused slope with the y-intercept.

Answer

Fractional slopes are not permitted.

Answer

The student must compute slope using two points only.

Question 15

Logic Problem

Passage

A student expands

y=\frac{2}{3}x-4

as

\frac{3}{2}

.

Question

What is the student’s error?

Accepted Answer

The student failed to distribute 4 to the -2

Answer

The student incorrectly combined like terms

Answer

The student should have divided by 4 before distributing

Answer

The student changed the slope by simplifying

Question 16

Logic Problem

Passage

A student claims: “The graph of $y=\frac{2}{3}x-4$ has slope 0 and y-intercept 7.”

Question

Is the student correct?

Accepted Answer

Yes, the slope is 0 and y-intercept is 7.

Answer

No, the slope is 7.

Answer

No, horizontal lines have no y-intercept.

Answer

No, the slope is undefined.

Question 17

Logic Problem

Passage

A student states: “If a line has slope 0, then it cannot cross the x-axis.”

Question

Is the statement always true?

Accepted Answer

No, because $y=0$ has slope 0 and lies on the x-axis

Answer

Yes, because any line with slope 0 stays above or below the x-axis

Answer

No, because slope 0 means the line is vertical

Answer

Yes, because slope 0 implies the line has no intercepts

Question 18

Logic Problem

Passage

A student says: “If the y-intercept is −3, then the line passes through (−3, 0).”

Question

Is the student’s interpretation correct?

Accepted Answer

No, because the y-intercept point is

y=2x-3

Answer

No, because a y-intercept cannot be negative

Answer

Yes, because the y-intercept is always written as $y+4=-3(x-2)$

Answer

Yes, because swapping coordinates does not change intercept meaning

Question 19

Logic Problem

Passage

A student computes the slope between $y=\frac{2}{3}x-4$ and $\frac{3}{2}$ as $\frac{7}{0}$ , then concludes, "The slope is 0 because the denominator is 0.

Question

Is the student's final conclusion correct?

Accepted Answer

No, because division by 0 is undefined, indicating a vertical line

Answer

Yes, because a denominator of 0 makes the fraction equal 0

Answer

No, because the slope should be 7 whenever the y-values change by 7

Answer

Yes, because the slope of any vertical line is 0

Question 20

Logic Problem

Passage

A student concludes, “If the slope of a linear function is 0, then the function is constant and its graph is horizontal.”

Question

Is the student’s final conclusion correct?

Accepted Answer

Yes, because slope 0 means y does not change as x changes

Answer

Yes, because slope 0 means the line passes through the origin

Answer

No, because a constant function must have undefined slope

Answer

No, because slope 0 corresponds to a vertical line

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