Q:

The table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. x f(x) 0 1 2 9 4 17 g(x) = 3x + 1

Accepted Solution

A:
Answer:The y-intercepts of both functions are the same and the function f(x) has a greater slope than the function g(x)Step-by-step explanation:we know thatThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] step 1Determine the slope of the function f(x)take two points from the table(0,1) and (2,9)substitute in the formula[tex]m=\frac{9-1}{2-0}[/tex] [tex]m=\frac{8}{2}[/tex] [tex]m_1=4[/tex] Remember that the y-intercept is the value of y when the value of x is equal to zeroIn this problem the point (0,1) is the y-interceptso[tex]b_1=1[/tex]step 2Determine the slope of the function g(x)we have[tex]g(x)=3x+1[/tex]This is the equation of the line in slope intercept form[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptsoIn this problem[tex]m_2=3[/tex][tex]b_2=1[/tex]step 3Compare the y-intercepts and slopes[tex]b_1=b_2\\m_1 > m_2[/tex]The y-intercepts of both functions are the same and the function f(x) has a greater slope than the function g(x)