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

Study Guide - Practice Questions

Study Guide - Flashcards