Respuesta :
SOLUTION
Given the information in the question, the following steps help to solve the question
Step 1: Write out the mathematical interpretations of the statements:
After 2 hours, Rachel is 13 miles from the campground.
After 4 hours, Rachel is 6 miles from the campground.
Step 2: Write the interpretations in form of points, we have:
x as the number of hours and y as the number of miles from the campground.
Therefore, we have two points (2,13) and (4,6).
[tex](x_1,y_1_{})(x_2,y)=(2,13)and(4,6)[/tex]Step 3: We find the slope of the graph using the point gotten:
The equation of the line passing through the points is:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1_{}}(x-x_{1)} \\ y-13=\frac{6-13}{4-2}(x-2) \\ y-13=\frac{-7}{2}(x-2) \\ y-13=-3.5(x-2) \\ y-13=-3.5x+7 \\ y=-3.5x+7+13 \\ y=-3.5x+20 \end{gathered}[/tex]Step 4: Get the slope using the general equation of a line
[tex]\begin{gathered} y=bx+c \\ \text{where b is the slope and c is the y-intercept} \\ \text{if }y=-3.5x+20 \\ \text{then, slope(b)=-3.5} \end{gathered}[/tex]Hence, the slope of the graph is -3.5 and this means that the rate at which Rachel's distance from the campground changes per hour is 3.5 miles which is option B.
