Question

Consider the graph below.

Which of the following represent the equation in point-slope form? Select TWO that apply!

A. y + 2 = 1/3(x + 2)

B. y = 1/3(x - 4)

C. y + 2 = 3 (x + 2)

D. y = 3 (x - 4)

E. y - 2 = 1/3(x - 2)

F. y = 1/3(x + 4)

Answer 1

Option E and F are correct.

Explanation:

`$$Let's consider the formula for point slope form\begin{center}\\$y-y_1=m(x-x_1)$\\\end{center}\\Here, $y_1$ equals any known y-coordinate of a point that lies on the line. $x_1$ equals any known x-coordinate of a point that lies on the line. $m$ is equal to the slope of the line.`

`$$\textbf{Step 1.} Find the slope of the graph. \\To find the slope, we will utilize the formula for the slope of 2 points:\\\begin{center} $(y_2-y_1)/(x_2-x_1)$\end{center}\\We'll plug in 2 known points shown: (2,2) and (-4,0) (note that you could use any two points given on the graph). The expression becomes: \\\begin{center}$(0-2)/(-4-2)$\\$=(-2)/(-6)$\\=$(1)/(3)$\end{center}\\Since $m=(1)/(3)$ in the point-slope formula, this narrows down the options to A, B, E, and F.`

`$$\textbf{Step 2.} Use process of elmination. \begin{itemize}\\\item Option \textbf{A} represents the point (-2,-2), which is not on the line. \item Option \textbf{B} represents the point (0,4), which is not on the line.\item Option \textbf{E} represents the point (2,2), which \textit{is} on the line.\item Option \textbf{F} represents the point (-4,0), which \textit{is} on the line.\\`

`$$\textbf{Solution.} Since Option \textbf{E} and Option \textbf{F} both contain points that lie on the line with the correct slope, \fbox{Option \textbf{E} and \textbf{F} are correct.}`