11 - 8 = 3
14 - 11 = 3
17 - 14 = 3
If x increases by increases by 1, y increases by increases by 3, so this is a linear function.
Slope for any linear function is:
m = ( yA - yB ) / ( xA - xB )
where:
xA, yA is first point
xB, yB is second point
You can choose any two points e.g.
xA = 1 , yA = 8
xB = 3 , yB = 14
m = ( yA - yB ) / ( xA - xB ) = ( 14 - 8 ) / ( 3 - 1 ) = 6 / 2 = 3
The slope-intercept form of a straight line:
y = m x + b
In this case:
y = 3 x + b
Select any point to calculate the value of b.
e.g.
x = 4 , y = 17
y = 3 x + b
17 = 3 ∙ 4 + b
17 = 12 + b
Subtract 12 to both sides
5 = b
b = 5
So:
y = m x + b
y = 3 x + 5
Answer B
Which function rule represents the input-output table?
x | y
1 | 8
2 | 11
3 | 14
4 | 17
A: h(x)=-3x-5
B: h(x)=3x+5
C: h(x)=-3x+5
D: h(x)=3x-5
2 answers
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