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Function A and Function B are linear functions. Function A x y -8 2 -4 3 8 6 Function B y = (1/2)x + 1 Which statement is true? The y-intercept of Function A is greater than the y-intercept of Function B. The y-intercept of Function A is less than the y-intercept of Function B

Quizzma Team

Function A and Function B are linear functions.

Function A
x y
-8 2
-4 3
8 6

Function B
y = (1/2)x + 1

Which statement is true?
The y-intercept of Function A is greater than the y-intercept of Function B.
The y-intercept of Function A is less than the y-intercept of Function B.




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    1 Answer

    1. Quizzma Team

      To determine the y-intercept of Function A, we need to find the point where the line crosses the y-axis (where x = 0).

      From the given points of Function A:

      – When ( x = -8 ), ( y = 2 )

      – When ( x = -4 ), ( y = 3 )

      – When ( x = 8 ), ( y = 6 )

      We can calculate the slope (m) between two of these points, say (-4, 3) and (8, 6):

      [

      m = frac{y_2 – y_1}{x_2 – x_1} = frac{6 – 3}{8 – (-4)} = frac{3}{12} = frac{1}{4}

      ]

      Using the slope, we can express the linear equation of Function A in slope-intercept form ( y = mx + b ).

      We can use one of the points, such as (-4, 3), to find the y-intercept (b):

      [

      3 = frac{1}{4}(-4) + b

      ]

      [

      3 = -1 + b

      ]

      [

      b = 4

      ]

      So, the y-intercept of Function A is ( 4 ).

      For Function B, the equation is given as:

      [

      y = frac{1}{2}x + 1

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