The equation 6y-3x=5 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 (5)/(6) and its y-intercept is -(5)/(3). (B) The graph's x-intercept is -(5)/(3) and its y-intercept is (5)/(6) (C) The graph has a slope of 2 . (D) The graph has a slope of -(1)/(2).

Finding the x-intercept: To find the x-intercept, set y = 0 in the equation 6y - 3x = 5 and solve for x. 6(0) - 3x = 5 -3x = 5 x = -5/3Finding the y-intercept: To find the y-intercept, set x = 0 in the equation 6y - 3x = 5 and solve for y. 6y - 3(0) = 5 6y = 5 y = 5/6Finding the slope of the graph: To find the slope of the graph, rewrite the equation in slope-intercept form (y = mx + b), where m is the slope. 6y - 3x = 5 6y = 3x + 5 y = (3/6)x + 5/6 y = (1/2)x + 5/6 The slope of the graph is 1/2.

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The equation
6y-3x=5 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
(5)/(6) and its
y-intercept is
-(5)/(3).
(B) The graph's
x-intercept is
-(5)/(3) and its
y-intercept is
(5)/(6)
(C) The graph has a slope of 2 .
(D) The graph has a slope of
-(1)/(2).

The equation $6 y-3 x=5$ 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 $\frac{5}{6}$ and its $y$ -intercept is $-\frac{5}{3}$ . $\newline$ (B) The graph's $x$ -intercept is $-\frac{5}{3}$ and its $y$ -intercept is $\frac{5}{6}$ . $\newline$ (C) The graph has a slope of $2$ . $\newline$ D The graph has a slope of $-\frac{1}{2}$ .

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Math Problems

Algebra 1

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

Full solution

Q. The equation

6 y-3 x=5

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

\frac{5}{6}

and its

y

-intercept is

-\frac{5}{3}

\newline

(B) The graph's

x

-intercept is

-\frac{5}{3}

and its

y

-intercept is

\frac{5}{6}

\newline

2

\newline

D The graph has a slope of

-\frac{1}{2}

Finding the x-intercept: To find the x-intercept, set $y = 0$ in the equation $6y - 3x = 5$ and solve for $x$ . $\newline$ $6(0) - 3x = 5$ $\newline$ $-3x = 5$ $\newline$ $x = -\frac{5}{3}$
Finding the y-intercept: To find the y-intercept, set $x = 0$ in the equation $6y - 3x = 5$ and solve for $y$ . $\newline$ $6y - 3(0) = 5$ $\newline$ $6y = 5$ $\newline$ $y = \frac{5}{6}$
Finding the slope of the graph: To find the slope of the graph, rewrite the equation in slope-intercept form $y = mx + b$ , where $m$ is the slope. $\newline$ $6y - 3x = 5$ $\newline$ $6y = 3x + 5$ $\newline$ $y = \frac{3}{6}x + \frac{5}{6}$ $\newline$ $y = \frac{1}{2}x + \frac{5}{6}$ $\newline$ The slope of the graph is $\frac{1}{2}$ .
Check the given options: Option $A$ : The graph's $x$ -intercept is not $\frac{5}{6}$ and its $y$ -intercept is not $-\frac{5}{3}$ . Therefore, option $A$ is incorrect. $\newline$ Option $B$ : The graph's $x$ -intercept is $-\frac{5}{3}$ and its $y$ -intercept is $\frac{5}{6}$ . Therefore, option $B$ is correct. $\newline$ Option $C$ : The graph does not have a slope of $2$ . Therefore, option $C$ is incorrect. $\newline$ Option $D$ : The graph does not have a slope of $-\frac{1}{2}$ . Therefore, option $D$ is incorrect.