Use the table to answer the question.
X. Y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
(1 point)
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y = 10x - 2
y = 10x + 2
y = - 10x + 78
y = x + 34
To find the equation of the linear function that models the relationship shown in the table, we need to determine the slope and y-intercept.
First, we can calculate the slope using the coordinates (4, 38) and (6, 58):
Slope (m) = (change in y) / (change in x) = (58 - 38) / (6 - 4) = 20 / 2 = 10
Next, we can substitute one of the points into the slope-intercept form of a linear equation, y = mx + b, to solve for the y-intercept (b). Let's use the point (4, 38):
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2
Now we have both the slope (m = 10) and the y-intercept (b = -2), so we can write the equation of the linear function that models the relationship shown in the table as:
y = 10x - 2
Therefore, the correct equation is y = 10x - 2.