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The equation
5x+10 y=30 is graphed in the
xy-plane. Which of the statements below is true of its graph?
Choose 1 answer:
(A) The graph's
x-intercept is 3 and its
y-intercept is 6 .
(B) The graph has a slope of
(1)/(2).
(c) The graph has a slope of
-(2)/(1).
(D) The graph's
x-intercept is 6 and its
y-intercept is 3 .

The equation $5 x+10 y=30$ is graphed in the $x y$ -plane. Which of the statements below is true of its graph? $\newline$ Choose $1$ answer: $\newline$ (A) The graph's $x$ -intercept is $3$ and its $y$ -intercept is $6$ . $\newline$ (B) The graph has a slope of $\frac{1}{2}$ . $\newline$ (C) The graph has a slope of $-\frac{2}{1}$ . $\newline$ D The graph's $x$ -intercept is $6$ and its $y$ -intercept is $3$ .

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

Full solution

Q. The equation

5 x+10 y=30

is graphed in the

x y

-plane. Which of the statements below is true of its graph?

\newline

Choose

1

answer:

\newline

(A) The graph's

x

-intercept is

3

and its

y

-intercept is

6

.

\newline

(B) The graph has a slope of

\frac{1}{2}

.

\newline

(C) The graph has a slope of

-\frac{2}{1}

.

\newline

D The graph's

x

-intercept is

6

and its

y

-intercept is

3

.

Find y-intercept: To find the y-intercept, we set $x$ to $0$ and solve for $y$ . $\newline$ $5(0) + 10y = 30$ $\newline$ $10y = 30$ $\newline$ $y = \frac{30}{10}$ $\newline$ $y = 3$
Find x-intercept: To find the x-intercept, we set $y$ to $0$ and solve for $x$ . $5x + 10(0) = 30$ $5x = 30$ $x = \frac{30}{5}$ $x = 6$
Find slope: To find the slope, we need to rewrite the equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope. $\newline$ $5x + 10y = 30$ $\newline$ $10y = -5x + 30$ $\newline$ $y = (-5/10)x + 30/10$ $\newline$ $y = (-1/2)x + 3$ $\newline$ The slope is $-1/2$ .
Compare with answer choices: Now we can compare the information we found with the answer choices. $\newline$ (A) The graph's $x$ -intercept is $3$ and its $y$ -intercept is $6$ . (Incorrect, we found $x$ -intercept is $6$ and $y$ -intercept is $3$ ) $\newline$ (B) The graph has a slope of $\frac{1}{2}$ . (Incorrect, the slope is negative, $-\frac{1}{2}$ ) $\newline$ (C) The graph has a slope of $-\frac{2}{1}$ . (Incorrect, the slope is $-\frac{1}{2}$ , not $-\frac{2}{1}$ ) $\newline$ (D) The graph's $x$ -intercept is $6$ and its $y$ -intercept is $3$ . (Correct, matches our findings from Step1 & Step2)

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