Answer:
The slope of the line must be 3
Step-by-step explanation:
The picture of the question in the attached figure
step 1
we know that
The volume of a rectangular prism is equal to
[tex]V_r_p=Bh[/tex] ----> equation A
where
B is the area of the base of the prism
h is the height of the rectangular prism
step 2
The volume of a square pyramid is equal to
[tex]V_s_p=\frac{1}{3}Bh[/tex] -----> equation B
where
B is the area of the square base of pyramid
h is the height of the pyramid
step 3
substitute equation A in equation B
[tex]V_s_p=\frac{1}{3}V_r_p[/tex]
Find the relationship between the volume of a rectangular prism and the volume of a square pyramid
[tex]\frac{V_r_p}{V_s_p}=3[/tex]
therefore
The slope of the line must be 3
let's check it
To solve for the slope of the line, you must choose two coordinates first and use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Choosing the points (2,6) and (3,9)
substitute
[tex]m=\frac{9-6}{3-2}=3[/tex] ----> is correct
