Answer:
B and F
Step-by-step explanation:
Given
Functions A and B
Required
Select the true statements
First, determine the equation of A
We have:
[tex](x_1, y_1) = (1,2)[/tex]
[tex](x_2, y_2) = (3,10)[/tex]
Calculate slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{10 - 2}{3 - 1}[/tex]
[tex]m = \frac{8}{2}[/tex]
[tex]m =4[/tex]
So, the equation is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 4(x - 1) + 2[/tex]
[tex]y = 4x - 4 + 2[/tex]
[tex]y = 4x -2[/tex]
So, we have:
[tex]y = 4x -2[/tex] ------ A
[tex]y = 3x + 4[/tex] ---- B
The y intercept is when [tex]x = 0[/tex]
So, we have:
[tex]y = 4 * 0 - 2 = -2[/tex] ---- y intercept of A
[tex]y = 3 * 0 + 4 = 4[/tex] ---- y intercept of B
By comparison:
[tex]-2 < 4[/tex]
Hence: (b) is correct
The rate of change of a function [tex]y = mx + b[/tex] is m
So:
The rate of change of A is:
[tex]m_A=4[/tex]
and for B is:
[tex]m_B=3[/tex]
By comparison:
[tex]4 > 3[/tex]
Hence: (F) is correct
