Question

This table shows a linear relationship. x 3 4 5 6 7 y 14 18 22 26 30 Based on the information in this table, which equation can be used to model the relationship between x and y? Responses y = 4x + 2 y, = 4, x, + 2 y = 2x + 4 y, = 2, x, + 4 y = 4x y, = 4, x y = 2x

Answer 1

Explanation:

y = mx + b

Where:

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, 14) and (7, 30):

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

m = (30 - 14) / (7 - 3)

m = 16 / 4

m = 4

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

y = 4x + b

To find the y-intercept (b), we can use one of the points from the table. Let's use the point (3, 14):

14 = 4(3) + b

14 = 12 + b

Now, solve for b:

b = 14 - 12

b = 2

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

y = 4x + 2

Therefore, the correct equation is: y = 4x + 2.

Answer 2

4x +2 I used casework