The description below represents Function A and the table represents Function B: Function A The function is 8 more than 3 times x. Functi

Question

The description below represents Function A and the table represents Function B: Function A The function is 8 more than 3 times x. Function B x y −1 2 0 5 1 8 Which statement is correct about the slope and intercept of the two functions? (1 point) Their slopes are equal but y-intercepts are not equal. Their slopes are not equal but y-intercepts are equal. Both slopes and y-intercepts are equal. Neither slopes nor y-intercepts are equal.

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    2021-09-10T06:44:07+00:00

    Answer: first option, their slopes are equal but y-intercepts are not equal.

    Justification:

    1) Function A

    The function is 8 more than 3 times x. => y = 8 + 3x

    2) Function B

      x      y

    −1      2

      0      5

      1     8

    3) Slope and y intercept of y = 8 + 3x

    That equation is the slope – intercept form of the line.

    The general equation is y = mx + b, where m is the slope and b is the y-intercept.

    So, in y = 8 + 3x, the slope is 3 and the y-intercept is 8

    4) slope of the function B:

    slope = rise / run = Δy / Δx

    slope = [5 – 2] / [ 0 – (-1) ] = 3 / 1 = 1

    Also, slope = [ 8 – 5] / [1 – 0] = 3 / 1 = 3

    Also, slope = [ 8 – 2] / [1 – (-1)] = 6 / 2 = 3

    So, definetly the points represent a linear function with slope 3.

    The y-intercept is the value of y when x = 0. From the table y = 5 when x = 0, so the y – intercept is 5.

    5) Summarizing:

    Function     slope       y – intercept

    A                   3                   8

    B                   3                   5

    From which you conclude that: their slopes are equal but y-intercepts are not equal.

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