Answer:
Part a) Ernest's calculation was correct
Part b) Ernest's calculation was correct
Step-by-step explanation:
The picture of the question in the attached figure
The complete question is
Ernest calculated the slope of the graph during the uphill climb to be 10. His work is shown below.
Points: (60.900). (15, 450)
Slope : 900-450/60-15=450/45=10
Part a) Determine whether his calculation was correct or incorrect, and then explain why.
Part b) Confirm or disprove Ernest's work by selecting two different points and applying the slope formula. be sure to identify the points you chose
Part a)
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
A(60,900),B(15,450)
Remember that
[tex]m_A_B=m_B_A[/tex]
step 1
Find [tex]m_A_B[/tex]
substitute in the formula
[tex]m_A_B=\frac{450-900}{15-60}\\\\m_A_B=\frac{-450}{-45}=10[/tex]
step 2
Find [tex]m_B_A[/tex]
substitute in the formula
[tex]m_B_A=\frac{900-450}{60-15}\\\\m_B_A=\frac{450}{45}=10[/tex]
therefore
Ernest's calculation was correct, because [tex]m_A_B=m_B_A[/tex]
Part b) selecting two different points
we take the points
(0,300) and (50,800) -----> see the attached figure
substitute in the formula of slope
[tex]m=\frac{800-300}{50-0}[/tex]
[tex]m=\frac{500}{50}[/tex]
[tex]m=10[/tex]
therefore
Ernest's calculation was correct
