Answer:
The rate of change of f(x) is greater than that of g(x)
They have the same y intercept of 14
Step-by-step explanation:
Given
[tex]g(x) = -\frac{1}{2}x + 14[/tex]
Table for function f(x)
Required
Compare their rate of change and intercept
For g(x), we have:
[tex]g(x) = -\frac{1}{2}x + 14[/tex]
The form of an equation is:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
[tex]b =y\ intercept[/tex]
So:
[tex]m = -\frac{1}{4}[/tex]
[tex]b = 14[/tex]
For f(x): Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{17-16}{6-4}[/tex]
[tex]m = \frac{1}{2}[/tex]
The intercept is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (-2,13)[/tex]
[tex](x_2,y_2) = (0,y)[/tex] --- we want to solve for y
So:
[tex]\frac{1}{2} = \frac{y - 13}{0 --2}[/tex]
[tex]\frac{1}{2} = \frac{y - 13}{2}[/tex]
Multiply both sides by 2
[tex]1 =y - 13[/tex]
Make y the subject
[tex]y =1 + 13[/tex]
[tex]y = 14[/tex]
So, we have:
[tex]m = -\frac{1}{4}[/tex] and [tex]b = 14[/tex] -- for g(x)
[tex]m = \frac{1}{2}[/tex] and [tex]y = 14[/tex] --- for f(x)
By comparison:
The rate of change (i.e. slope) of f(x) is greater than that of g(x) because [tex]1/2 > -1/2[/tex]
They have the same y intercept of 14
