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) Responses y=10x−2 y equals 10 x minus 2 y=10x+2 y equals 10 x plus 2 y=−10x+78 y equals negative 10 x plus 78 y=x+34

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).

1. Calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):

   Let \( (x_1, y_1) = (4, 38) \) and \( (x_2, y_2) = (6, 58) \).

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

2. Use the slope-intercept form \( y = mx + b \). We already have \( m = 10 \), so we plug that into the equation:

   \[ y = 10x + b \]

3. Substitute one of the points to find \( b \). Using the point (4, 38):

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

   \[ 38 = 40 + b \]

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

4. Write the final equation:

   \[ y = 10x - 2 \]

So the correct response is:

y = 10x - 2.