MATH SOLVE

2 months ago

Q:
# Help please.The equation represents function A, and the graph represents function B.Function A:F(x) = -2x + 1Function B:Which equation best compares the slope of the two functions?1. Slope of function B =2x slope of function A2. Slope of function A = slope of function B3. Slope of function A= 2x slope of function B4. Slope of function B = -slope of function A

Accepted Solution

A:

Answer:4. Slope of function B = -slope of function AStep-by-step explanation:Given:Function A is given as:[tex]F(x)=-2x+1[/tex]The above equation is of the form [tex]y=mx+b[/tex], where [tex]m[/tex] represents slope of the line.Therefore, on comparing the function A with the above standard form, er conclude that, slope of function A is -2.Now, from the graph of function, we consider any two points on the graph and determine the slope of the line using the two points.Let us consider the points [tex](x_1,y_1)=(1.5,0)\ and\ (x_2,y_2)=(3,3)[/tex]Now, the slope of the line passing through these two points is given as:[tex]m_B=\frac{y_2-y_1}{x_2-x_1}=\frac{3-0}{3-1.5}=\frac{3}{1.5}=2[/tex]Therefore, slope of function B is 2.Therefore, the correct relation between the slopes of the two functions is that the slope of function B is negative of the slope of function A.[tex]m_B=-(m_A)=-(-2)=2[/tex]