Solution
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
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=0 \\ y_1=1 \\ x_2=2 \\ y_2=11 \end{gathered}[/tex][tex]\begin{gathered} \frac{11-1}{2-0} \\ \\ \frac{10}{2} \\ \\ 5 \end{gathered}[/tex]
For f(x)
y - intercept = 1
slope = 5
Let us proceed with g(x)
[tex]\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}[/tex]
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)
