Question

Big ideas math assignment help please!!!!

Answer 1

Option C

Explanation:

`$$We're tasked with finding the graphical representation of $y=-(3)/(2)x$. \\To understand how to do this, let's examine the slope intercept formula:\begin{center}$y=mx+b$\end{center}Here, $m$ is the slope of the line, and $b$ is the y-intercept. In the given equation $y=-(3)/(2)x$, $-(3)/(2)$ is the slope, and 0 is the y-intercept. Which graph contains these properties?`

`$$ To determine which graph has a slope of $-(3)/(2)$, one method is to use the slope formula $(y_2-y_1)/(x_2-x_1)$, where $(x_1,y_1)$ and $(x_2,y_2)$ are 2 points along the line.\begin{itemize}\item\textbf{Option A:} There is no need to find the slope of this graph as it has a y-intercept of 2 which does not agree with our equation.\item\textbf{Option B:} Plugging in the points (0,0) and (2,3) into the slope formula:\begin{center}$(3-0)/(2-0)\\$=(3)/(2)$\end{center}`
`$$Hence, the slope of graph B $=(3)/(2)\\eq -(3)/(2).$\begin{itemize}\item \textbf{Option C:} Plugging in the points (-2,3) and (0,0) into the slope formula:\begin{center}$(0-3)/(0-(-2))$\\=$-(3)/(2)$\end{center} Hence, the slope of graph C $=-(3)/(2)$, which agrees with our equation. So \textbf{Option C} is correct.`