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

Full solution

Q. The equation

\newline

(y-2)=\frac{1}{5}(x+5)

is graphed in the

xy

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

\newline

Choose

1

answer:

\newline

(A) The graph has a slope of

-5

and a

y

-intercept of

5

\newline

(B) The graph has a slope of

-5

and passes through the point

(2,-5)

\newline

\frac{1}{5}

and passes through the point

(-5,2)

\newline

(D) The graph has a slope of

\frac{1}{5}

and a

y

-intercept of

5

Identify Equation Form: Identify the slope-intercept form of the equation. $\newline$ The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Rewrite in Slope-Intercept Form: Rewrite the given equation in slope-intercept form. $\newline$ Starting with $y-2=\frac{1}{5}(x+5)$ , we add $2$ to both sides to isolate $y$ : $y = \frac{1}{5}(x+5) + 2$ .
Simplify Equation: Simplify the equation to identify the slope and y-intercept. $\newline$ We can distribute the $(1)/(5)$ across $(x+5)$ to get $y = (1)/(5)x + (1)/(5)\cdot5 + 2$ . Simplifying further, we get $y = (1)/(5)x + 1 + 2$ , which simplifies to $y = (1)/(5)x + 3$ .
Identify Slope: Identify the slope from the simplified equation. $\newline$ The coefficient of $x$ in the equation $y = \frac{1}{5}x + 3$ is $\frac{1}{5}$ , which is the slope of the line.
Identify Specific Point: Identify a specific point through which the graph passes. $\newline$ The equation was initially given as $(y-2)=\frac{1}{5}(x+5)$ . Setting $x$ to $-5$ , we get $(y-2)=\frac{1}{5}(-5+5)$ , which simplifies to $(y-2)=0$ . Adding $2$ to both sides gives us $y = 2$ . Therefore, when $x = -5$ , $y = 2$ , which means the graph passes through the point $(-5, 2)$ .
Choose Correct Statement: Choose the correct statement based on the identified slope and point. $\newline$ The graph has a slope of $(\frac{1}{5})$ and passes through the point $(-5, 2)$ , which corresponds to option (C).