To find the equation of a linear function, we need to determine the slope and the y-intercept.
To find the slope, we use the formula:
slope = (change in y) / (change in x)
For the given table, the change in y is:
10 - (-3) = 13
And the change in x is:
18 - 6 = 12
So the slope is:
slope = 13 / 12
Next, we can find the y-intercept by substituting one of the points into the equation y = mx + b and solving for b. Let's use the point (6, -3):
-3 = (13/12)(6) + b
Simplifying this equation:
-3 = 13/2 + b
To solve for b, we subtract 13/2 from both sides:
(-3) - (13/2) = b
To simplify, we need a common denominator:
(-6/2) - (13/2) = b
-19/2 = b
Finally, we have the slope (13/12) and the y-intercept (-19/2), so we can write the equation of the linear function as:
y = (13/12)x - 19/2
Use the table to answer the question. x y 18 10 6 −3 Write the equation of the linear function represented by the table.
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