Question 1

Which of the following statements best describes the solution set of the equation $$x + y = 5$$?

Accepted Answer

It is a set of many points $$(x, y)$$ that form a line on a 2D plane.

Question 2

Given the equation $$y = 2x - 1$$, which of the following ordered pairs is a solution?

Accepted Answer

$$(1, 1)$$

Question 3

If a point $$(x, y)$$ does NOT satisfy the equation of a line, what does this mean about its location relative to the graph?

Accepted Answer

It is not on the graph of the equation.

Question 4

Which of the following is the $$y-$$intercept of the equation $$y = -2x + 1$$?

Accepted Answer

$$(0, 1)$$

Question 5

A chemical reaction is modeled by the equation $$y = x^2$ + 3. If $$the concentration $$x = -1$$, what is the resulting $$y$$ value?

Accepted Answer

$$y = 4$$

Question 6

Which of the following points is an $$x-$$intercept of the graph of $$y = x^2$ - 4$$?

Accepted Answer

$$(2, 0)$$

Question 7

A medical researcher graphs the equation $$y = \sqrt{x} + 1 to $$model a dosage curve. Which $$x-$$value below is NOT valid for this equation?

Accepted Answer

$$x = -1$$

Question 8

Given the equation $$y = -x + 3$$, which of the following ordered pairs lies on the graph?

Accepted Answer

$$(2, 1)$$

Question 9

Which step is NOT part of the process for graphing a two-variable equation by plotting points?

Accepted Answer

Multiply all $$x-$$values by 2 before plotting.

Question 10

A business models profit with $$y = 2x + 5. $$What is the $$y-$$intercept, and what does it represent in this context?

Accepted Answer

$$(0, 5)$$; the profit when $$x = 0$$

Question 11

Which of the following is the correct $$x-$$intercept for the equation $$y = 3x - 6$$?

Accepted Answer

$$(2, 0)$$

Question 12

A student claims that the point $$(0, 3) is $$the $$x-$$intercept of the equation $$y = x + 3. Is $$this correct? Why or why not?

Accepted Answer

No, because the $$x-$$intercept occurs when $$y = 0$$, not $$x = 0.$$

Question 13

If the graph of an equation crosses the $$y-$$axis at $$(0, -2)$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -2)$$

Question 14

Which of the following points does NOT satisfy the equation $$y = x^2$ + 1$$?

Accepted Answer

$$(1, 1)$$

Question 15

A scientist is graphing $$y = -x^2$ + 4. $$What is the $$y-$$intercept of this equation?

Accepted Answer

$$(0, 4)$$

Question 16

Which of the following is a correct ordered pair for the equation $$y = \sqrt{x} + 1$$?

Accepted Answer

$$(4, 3)$$

Question 17

If a graph crosses the $$x-$$axis at $$x = -3.5$$, what is the $$x-$$intercept as an ordered pair?

Accepted Answer

$$(-3.5, 0)$$

Question 18

A real-world scenario: The height $$y (in $$meters) of a ball thrown upward is modeled by $$y = -x^2$ + 4x + 1$$, where $$x is $$time in seconds. What is the height at $$x = 2$$ seconds?

Accepted Answer

$$y = 5$$

Question 19

Which of the following best describes the $$x-$$intercept of a graph?

Accepted Answer

The point where the graph crosses the $$x-$$axis, where $$y = 0.$$

Question 20

If you are given the equation $$y = x + 2$$ and asked to plot points, which of the following is a correct step?

Accepted Answer

Choose several $$x-$$values, calculate corresponding $$y-$$values, and plot the $$(x, y)$$ pairs.

Graphing and Analyzing Equations with Two Variables

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