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Use the table to answer the question.

x y
18 10
6 −3
Write the equation of the linear function represented by the table.

(1 point)
Responses

y=(1312)x−(192)
y equals left parenthesis Start Fraction 13 over 12 End Fraction right parenthesis x minus Start Fraction 19 over 2 End Fraction right parenthesis

y=(1213)x−(11113)
y equals left parenthesis Start Fraction 12 over 13 End Fraction right parenthesis x minus Start Fraction 111 over 13 End Fraction right parenthesis

y=−192
y equals Start Fraction negative 19 over 12 End Fraction

y=(−1312)x+(72)

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
11 months ago

None of the provided options correctly represent the linear function.

To find the equation of the linear function, we can use the formula for a line:

y = mx + b

where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (change in y) / (change in x)

Using the points (18, 10) and (6, -3), we can calculate the slope:

m = (10 - (-3)) / (18 - 6)
m = 13 / 12

Now we can substitute the slope and one of the points into the equation to find the y-intercept. Let's use the point (18, 10):

10 = (13 / 12)(18) + b

Solving for b, we get:

b = 10 - (13/12)(18)
b = 10 - 39/2
b = 20/2 - 39/2
b = -19/2

Thus, the equation of the linear function represented by the table is:

y = (13/12)x - 19/2