Equations of Linear Functions Quick Check

Question

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 plus 2

y=x+34
y equals x plus 34

y=10x−2
y equals 10 x minus 2

y=−10x+78

Answer 1

To find the equation of the linear function, we first need to find the slope (m) and y-intercept (b) using the given points (4,38) and (6,58).

m = (y2 - y1) / (x2 - x1)
m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10

Now that we have the slope, we can use it to find the y-intercept (b) using the point (4,38).
38 = 10(4) + b
38 = 40 + b
b = -2

So, the equation of the linear function is:
y = 10x - 2

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