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)

Question

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

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we can use the two data points 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 linear equation: We use one of the points (let's use (4, 38)) and the slope we just calculated. \[ y - y_1 = m(x - x_1) \] Substituting in the values: \[ y - 38 = 10(x - 4) \]

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

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