Use the table to answer the question.

Question

x
y

4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.

(1 point)
Responses

y=10x+2
y equals 10 x plus 2

y=10x−2
y equals 10 x minus 2

y=x+34
y equals x plus 34

y=−10x+78
y equals negative 10 x plus 78
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Answer 1

To find the equation of the linear function that models the relationship shown in the table, we can use the coordinates provided:

1. (4, 38)
2. (6, 58)

First, we calculate the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (4, 38) and (6, 58):

• \(x_1 = 4, y_1 = 38\)
• \(x_2 = 6, y_2 = 58\)

Now plug in the values: \[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]

Now we have the slope \(m = 10\).

Next, we can use the point-slope form of the equation, which is: \[ y - y_1 = m(x - x_1) \]

Using the point (4, 38): \[ y - 38 = 10(x - 4) \]

Distributing the 10: \[ y - 38 = 10x - 40 \]

Adding 38 to both sides: \[ y = 10x - 2 \]

Thus, the equation of the linear function that models the relationship shown in the table is:

y = 10x - 2

So the correct response is: y = 10x − 2