The equations 2y=-4x+8 and 2y=-4x+16 are graphed in the xy-plane. Which of the following must be true of the graphs of the two equations? Choose 1 answer: (A) The graphs of the two equations are parallel lines. (B) The graphs of the two equations are perpendicular lines. (C) The graphs have the same y-intercept. (D) The y-intercepts of the two graphs are reflected in the x-axis.

Analyze First Equation: Let's analyze the first equation 2y = -4x + 8. To find the slope and y-intercept, we can put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Divide both sides by 2 to isolate y. y = -2x + 4 The slope (m) is -2 and the y-intercept (b) is 4.Analyze Second Equation: Now let's analyze the second equation 2y = -4x + 16. Again, we put it in slope-intercept form by dividing both sides by 2. y = -2x + 8 The slope (m) is -2 and the y-intercept (b) is 8.Comparison of Equations: Comparing the two equations, we see that they both have the same slope, -2, but different y-intercepts, 4 and 8, respectively. Since they have the same slope, the lines are parallel to each other.Check Answer Choices: Now let's check the answer choices against our findings: (A) The graphs of the two equations are parallel lines. This is true based on our analysis. (B) The graphs of the two equations are perpendicular lines. This is false because perpendicular lines have slopes that are negative reciprocals of each other. (C) The graphs have the same y-intercept. This is false because the y-intercepts are 4 and 8. (D) The y-intercepts of the two graphs are reflected in the x-axis. This is false because reflection in the x-axis would not change the y-intercept's absolute value, only its sign.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equations $\newline$ $2y = -4x + 8$ and $\newline$ $2y = -4x + 16$ $\newline$ are graphed in the $xy$ -plane. Which of the following must be true of the graphs of the two equations? $\newline$ Choose $1$ answer: $\newline$ (A) The graphs of the two equations are parallel lines. $\newline$ (B) The graphs of the two equations are perpendicular lines. $\newline$ (C) The graphs have the same $y$ -intercept. $\newline$ (D) The $y$ -intercepts of the two graphs are reflected in the $x$ -axis.

View step-by-step help

Home

Math Problems

Algebra 1

Reflections of functions

Full solution

Q. The equations

\newline

2y = -4x + 8

and

\newline

2y = -4x + 16

\newline

are graphed in the

xy

-plane. Which of the following must be true of the graphs of the two equations?

\newline

Choose

1

answer:

\newline

(A) The graphs of the two equations are parallel lines.

\newline

(B) The graphs of the two equations are perpendicular lines.

\newline

y

-intercept.

\newline

(D) The

y

-intercepts of the two graphs are reflected in the

x

-axis.

Analyze First Equation: Let's analyze the first equation $2y = -4x + 8$ . $\newline$ To find the slope and y-intercept, we can put it in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. $\newline$ Divide both sides by $2$ to isolate $y$ . $\newline$ $y = -2x + 4$ $\newline$ The slope ( $m$ ) is $-2$ and the y-intercept ( $b$ ) is $y = mx + b$ $0$ .
Analyze Second Equation: Now let's analyze the second equation $2y = -4x + 16$ . Again, we put it in slope-intercept form by dividing both sides by $2$ . $y = -2x + 8$ The slope ( $m$ ) is $-2$ and the y-intercept ( $b$ ) is $8$ .
Comparison of Equations: Comparing the two equations, we see that they both have the same slope, $-2$ , but different y-intercepts, $4$ and $8$ , respectively. $\newline$ Since they have the same slope, the lines are parallel to each other.
Check Answer Choices: Now let's check the answer choices against our findings: $\newline$ (A) The graphs of the two equations are parallel lines. This is true based on our analysis. $\newline$ (B) The graphs of the two equations are perpendicular lines. This is false because perpendicular lines have slopes that are negative reciprocals of each other. $\newline$ (C) The graphs have the same $y$ -intercept. This is false because the $y$ -intercepts are $4$ and $8$ . $\newline$ (D) The $y$ -intercepts of the two graphs are reflected in the $x$ -axis. This is false because reflection in the $x$ -axis would not change the $y$ -intercept's absolute value, only its sign.