Use the table to answer the question.x y 18106 −3 Write the equation of the linear function represented by the table.(1 point)Responsesy=(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 parenthesisy=−192y equals Start Fraction negative 19 over 12 End Fractiony=(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 parenthesisy=(−1312)x+(72)
To find the equation of the linear function represented by the table, we need to find the slope (m) and y-intercept (b).
From the table, we can see that when x is 18, y is 106. This gives us the point (18, 106).
Let's use the point-slope form of the equation: y - y1 = m(x - x1)
Using the point (18, 106), we can substitute the values:
y - 106 = m(x - 18)
Now let's find the value of the slope (m) by using another point from the table. When x is -3, y is 18106. This gives us the point (-3, 18106).
Using these two points, we can find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (18106 - 106) / (-3 - 18)
m = 18000 / -21
m = -857.1428571 (approximately)
Now, substitute the value of m into the equation:
y - 106 = -857.1428571(x - 18)
Next, let's simplify the equation:
y - 106 = -857.1428571x + 15428.5714286
Move the constant term to the other side:
y = -857.1428571x + 15434.5714286
Rounding the answer to the nearest whole number, the equation of the linear function represented by the table is:
y = -857x + 15435