Question

reasoning with parallel and perpendicular lines
madison is a developer, and her group is planning some additions to a new community development. currently there is just one straight road that passes through the development: moonbeam drive. the main highway is represented by the x - axis on the graph. north is at the top of the graph, and east is at the right.
study the map to complete each statement.
sundance avenue will run parallel to moonbeam drive 4 blocks north of the highway, through the point (0, 4). determine the slope of moonbeam drive on the map.
slope of moonbeam drive =\frac{0 - }{20 - }
=
write the function, s(x), that describes the path of sundance avenue on the map: s(x)=
madisons group will build a road that is perpendicular to both sundance avenue and moonbeam drive. the slope of the line representing this road on the map will be

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. For Moonbeam Drive, we have the points $(20,0)$ and $(0,16)$.

Step2: Calculate the slope of Moonbeam Drive

$m=\frac{0 - 16}{20 - 0}=\frac{-16}{20}=-\frac{4}{5}$

Step3: Find the function for Sundance Avenue

Since Sundance Avenue is parallel to Moonbeam Drive, it has the same slope $m =-\frac{4}{5}$ and passes through the point $(0,4)$. Using the slope - intercept form $y=mx + b$ (where $m$ is the slope and $b$ is the y - intercept), substituting $m =-\frac{4}{5}$ and $b = 4$, we get $s(x)=-\frac{4}{5}x+4$.

Step4: Find the slope of the perpendicular line

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=-1$. Let $m_1 =-\frac{4}{5}$, then $m_2=\frac{5}{4}$.

Answer:

slope of Moonbeam Drive: $-\frac{4}{5}$
$s(x)=-\frac{4}{5}x + 4$
slope of the perpendicular line: $\frac{5}{4}$