Question

graphically determine the slopes of the line segments that create `ACD. Write your final slopes in simplest form.

Answer 1

$\begin{gathered} \text{Slope}_{AD}=\frac{9}{11} \\ \text{Slope}_{CD}=\frac{1}{3} \\ \text{Slope}_{AC}=\frac{7}{2} \end{gathered}$

Explanation

The slope of a line is a measure of its steepness,it is change in y over change in x

$\text{slope}=\frac{change\text{ in y}}{\text{change in x}}$

Step 1

AD

so, check in the graph for the change in y and the change in x ( count the units)

as we can see:

change in y(green)= 9

change in x(red)=11

therefore

$\begin{gathered} \text{Slope}_{AD}=\frac{change\text{ in y }}{\text{change in x}} \\ \text{Slope}_{AD}=\frac{9}{11} \end{gathered}$

Step 2

now, do the same for segment CD

$\begin{gathered} \text{Slope}_{CD}=\frac{5}{15}=\frac{1}{3} \\ \text{Slope}_{CD}=\frac{1}{3} \end{gathered}$

Step 3

finally, segment AC

$\begin{gathered} \text{Slope}_{AC}=\frac{change\text{ in y(purple) }}{\text{change in }x(\text{yeloow)}} \\ \text{Slope}_{AC}=\frac{14}{4}=\frac{7}{2} \\ \text{Slope}_{AC}=\frac{7}{2} \end{gathered}$

I hope this helps you