Question

compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them

Answer 1

Let us first obtain the equation of the linear function of f(x)

The y-intercept of f(x) is the point on the graph of f(x) when x = 0 . This is the point 1 as seen from the table given

We will pick two points on f(x) in order to obtain its slope

( 0, 1 ) and ( 2 , 11 )

The slope formula is given as

`(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} x_1=0 \\ y_1=1 \\ x_2=2 \\ y_2=11 \end{gathered}`
`\begin{gathered} (11-1)/(2-0) \\ \\ (10)/(2) \\ \\ 5 \end{gathered}`

For f(x)

y - intercept = 1

slope = 5

Let us proceed with g(x)

`\begin{gathered} g(x)=4x+1 \\ slope=4 \\ at\text{ }y\text{ }intercept\text{ }x=0 \\ g(x)=4(0)+1 \\ g(x)=1 \end{gathered}`

For g(x)

y-intercept = 1

slope = 4

The correct answer is OPTION B

The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x)