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)
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