The equation 6-2y=x is graphed in the xy-plane. Which of the following is a true statement about the graph? Choose 1 answer: A The graph's x-intercept is 6 and its y-intercept is -2. (B) The graph's x-intercept is 6 and its y-intercept is 2 . (C) The graph has a slope of -2 . (D) The graph has a slope of -(1)/(2).

Find Slope and Y-Intercept: First, we need to find the slope and y-intercept of the graph of the equation 6-2y=x. To do this, we should rewrite the equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.Rewrite Equation in Slope-Intercept Form: We can start by isolating y on one side of the equation. We'll subtract 6 from both sides to get -2y = x - 6.Isolate y in the Equation: Next, we divide both sides by -2 to solve for y. This gives us y = -(1/2)x + 3. Now we can see that the slope (m) is -(1/2) and the y-intercept (b) is 3.Calculate Slope and Y-Intercept: To find the x-intercept, we set y to 0 and solve for x. So, we have 0 = -(1/2)x + 3. Multiplying both sides by -2 to get rid of the fraction, we have 0 = x - 6. Adding 6 to both sides, we find that x = 6.Find X-Intercept: Now we have the x-intercept, which is 6, and the y-intercept, which is 3 (not -2 or 2 as suggested in options A and B). The slope is -(1/2), which matches option D.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation
6-2y=x is graphed in the
xy-plane. Which of the following is a true statement about the graph?
Choose 1 answer:
A The graph's
x-intercept is 6 and its
y-intercept is
-2.
(B) The graph's
x-intercept is 6 and its
y-intercept is 2 .
(C) The graph has a slope of -2 .
(D) The graph has a slope of
-(1)/(2).

The equation $6-2 y=x$ is graphed in the $x y$ -plane. Which of the following is a true statement about the graph? $\newline$ Choose $1$ answer: $\newline$ (A) The graph's $x$ -intercept is $6$ and its $y$ -intercept is $-2$ . $\newline$ B The graph's $x$ -intercept is $6$ and its $y$ -intercept is $2$ . $\newline$ (C) The graph has a slope of $-2$ . $\newline$ D) The graph has a slope of $-\frac{1}{2}$ .

View step-by-step help

Home

Math Problems

Algebra 1

Write a quadratic function from its x-intercepts and another point

Full solution

Q. The equation

6-2 y=x

is graphed in the

x y

-plane. Which of the following is a true statement about the graph?

\newline

Choose

1

answer:

\newline

(A) The graph's

x

-intercept is

6

and its

y

-intercept is

-2

\newline

B The graph's

x

-intercept is

6

and its

y

-intercept is

2

\newline

-2

\newline

D) The graph has a slope of

-\frac{1}{2}

Problem Understanding: First, we need to find the slope and y-intercept of the graph of the equation $6-2y=x$ . To do this, we should rewrite the equation in slope-intercept form, which is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept.
Rewrite Equation in Slope-Intercept Form: We can start by isolating $y$ on one side of the equation. We'll subtract $6$ from both sides to get $-2y = x - 6$ .
Calculate Slope and Y-Intercept: Next, we divide both sides by $-2$ to solve for $y$ . This gives us $y = -\left(\frac{1}{2}\right)x + 3$ . $\newline$ Now we can see that the slope ( $m$ ) is $-\left(\frac{1}{2}\right)$ and the y-intercept ( $b$ ) is $3$ .
Find X-Intercept: To find the x-intercept, we set $y$ to $0$ and solve for $x$ . $\newline$ So, we have $0 = -\frac{1}{2}x + 3$ . $\newline$ Multiplying both sides by $-2$ to get rid of the fraction, we have $0 = x - 6$ . $\newline$ Adding $6$ to both sides, we find that $x = 6$ .
Matching with the Options: Option ( $A$ ): The $x$ -intercept is $6$ , but the $y$ -intercept is $3$ not $-2$ . So, option $A$ is not correct. $\newline$ Option ( $B$ ): The $x$ -intercept is $6$ , but the $y$ -intercept is $3$ not $2$ . So, option $B$ is not correct. $\newline$ Option ( $C$ ): The slope is not $-2$ . So, option $C$ is not correct. $\newline$ Option ( $D$ ): The slope is $-(\frac{1}{2})$ . So, option $D$ is correct.