Use the table to answer the question.

Question

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

y=10x−2
y
=
10
x
−
2
y equals 10 x minus 2

y=x+34
y
=
x
+
34
y equals x plus 34

y=10x+2

Answer 1

To find the equation of the linear function from the points in the table, we can use the coordinates provided: (4, 38) and (6, 58).

1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]

2. Use the point-slope form of the equation of a line: The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] Using the point (4, 38): \[ y - 38 = 10(x - 4) \]

3. Simplify the equation: \[ y - 38 = 10x - 40 \] \[ y = 10x - 2 \]

Thus, the equation of the linear function that models the relationship shown in the table is: \[ \boxed{y = 10x - 2} \]