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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 $-\frac{1}{2}$ .

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Write a linear equation from a slope and y-intercept

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

(C) The graph has a slope of

-2

.

\newline

(D) The graph has a slope of

-\frac{1}{2}

.

Convert Equation to Slope-Intercept Form: Convert the given equation to slope-intercept form. $\newline$ The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. To convert the given equation $6 - 2y = x$ to this form, we need to solve for $y$ .
Isolate y in Equation: Isolate y on one side of the equation. $\newline$ Starting with $6 - 2y = x$ , we can subtract $6$ from both sides to get $-2y = x - 6$ .
Divide by $-2$ to Solve: Divide both sides by $-2$ to solve for $y$ . Dividing both sides by $-2$ gives us $y = -\left(\frac{1}{2}\right)x + 3$ .
Identify Slope and Y-Intercept: Identify the slope and y-intercept from the equation. $\newline$ From the equation $y = -(\frac{1}{2})x + 3$ , we can see that the slope ( $m$ ) is $-\frac{1}{2}$ and the y-intercept ( $b$ ) is $3$ .
Determine X-Intercept: Determine the x-intercept. $\newline$ To find the x-intercept, we set $y$ to $0$ and solve for $x$ . Plugging $y = 0$ into the equation gives us $0 = -\left(\frac{1}{2}\right)x + 3$ . Solving for $x$ , we get $x = 6$ .
Evaluate Answer Choices: Evaluate the answer choices. $\newline$ (A) The graph's $x$ -intercept is $6$ and its $y$ -intercept is $-2$ . (Incorrect, the $y$ -intercept is $3$ ) $\newline$ (B) The graph's $x$ -intercept is $6$ and its $y$ -intercept is $2$ . (Incorrect, the $y$ -intercept is $3$ ) $\newline$ (C) The graph has a slope of $-2$ . (Incorrect, the slope is $6$ $3$ ) $\newline$ (D) The graph has a slope of $6$ $3$ . (Correct, as determined in Step $4$ )

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