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

GPT-4o mini · Answer

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).

Calculate the slope (m): $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10$
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: $y - 38 = 10 (x - 4)$
Simplify: $y - 38 = 10 x - 40$ $y = 10 x - 40 + 38$ $y = 10 x - 2$

The equation of the linear function that models the relationship shown in the table is: $y = 10 x - 2$