Functions W and Z are both linear functions of x. Which statement comparing the functions is true? Select all that apply. A. The
1 answer:
The correct options are:
B. The slope of Function W is greater than the slope of Function Z.
F. The y-intercept of Function W is greater than the y-intercept of Function Z.
Let's find the slope (m) and y-intercept (b) of each function to see which one compares the two functions accurately.
Function W:
The slope of Function B, using two points on the line, (0, -1) and (2, 0):
m = ( y₂ - y₁ )/ (x₂ - x₁ )
m = [ 0 - (- 1 )]/( 2- 0 ) = 0.5
The y-intercept will be when x = 0. Therefore, from the graph, the y-intercept is b = -1.
For Function Z:
The slope of Function Z, using two pairs of values from the table of values for function Z, ( 0, - 2 ) and ( 2, - 1.5 ):
m = ( y₂ - y₁ )/ (x₂ - x₁ )
m = ( - 1.5 - ( -2 ) )/( 2 - 0 )
m = 0.5/2 = 0.25
The y-intercept is the value of y when x = 0.
From the table when x = 0, y = - 2. Therefore, the y-intercept is b = - 2.
Thus, the following statements that compare both functions are TRUE:
B. The slope of Function W is greater than the slope of Function Z.
- This is TRUE because 0.5 is greater than 0.25.
F. The y-intercept of Function W is greater than the y-intercept of Function Z.
- This is TRUE because -1 is greater than -2.
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