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=x+34
y equals x plus 34

y=10x−2
y equals 10 x minus 2

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

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we can use the two points given: (4, 38) and (6, 58).

First, we need to calculate the slope (m) of the line using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the values from the points (4, 38) and (6, 58):

\[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]

Now that we have the slope (m = 10), we can use one of the points to find the y-intercept (b) using the equation of a line:

\[ y = mx + b \]

Using the point (4, 38):

\[ 38 = 10(4) + b \]

\[ 38 = 40 + b \]

Now, solve for b:

\[ b = 38 - 40 = -2 \]

Now, we can write the equation of the line:

\[ y = 10x - 2 \]

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

y = 10x - 2