Question

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+78
y equals negative 10 x plus 78

y=x+34
y equals x plus 34

y=10x+2
y equals 10 x plus 2

Answer 1

To write the equation of the linear function that models the relationship shown in the table, we need to determine the slope (m) and the y-intercept (b) of the linear function.

First, let's find the slope using the two data points in the table: (4, 38) and (6, 58).
slope (m) = (y2 - y1) / (x2 - x1)
slope (m) = (58 - 38) / (6 - 4)
slope (m) = 20 / 2
slope (m) = 10

Next, let's substitute the slope (m) and one of the points, for example (4, 38), into the slope-intercept form of a linear equation: y = mx + b to find the y-intercept (b).
Using (4, 38):
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2

Now we have the slope (m = 10) and the y-intercept (b = -2), we can write the equation of the linear function that models the relationship:
y = 10x - 2

Therefore, the correct answer is:
y = 10x - 2