Question

This table shows a linear relationship. x 3 6 9 12 15 y 255 510 765 1020 1275 Based on the information in this table, which equation can be used to model the relationship between x and y? Responses y = 3x + 255 y, = 3, x, + 255 y = 85x y, = 85, x y = x + 3 y, = , x, + 3 y = 3x

Answer 1

Explanation:

y is the dependent variable (in this case, the values in the "y" column).

x is the independent variable (in this case, the values in the "x" column).

m is the slope of the line.

b is the y-intercept (the value of y when x is 0).

We can calculate the slope (m) using two points from the table. Let's use the points (3, 255) and (15, 1275):

m = (y2 - y1) / (x2 - x1)

m = (1275 - 255) / (15 - 3)

m = 1020 / 12

m = 85

Now that we have found the slope (m), we can determine the equation:

y = 85x + b

To find the y-intercept (b), we can use one of the points from the table. Let's use the point (3, 255):

255 = 85(3) + b

255 = 255 + b

Now, solve for b:

b = 255 - 255

b = 0

So, the equation that models the relationship between x and y in the table is:

y = 85x + 0

Since adding 0 to any number doesn't change it, we can simplify the equation to:

y = 85x

Therefore, the correct equation is: y = 85x.