Question

determine any data values that are missing from the table, assuming that the data represent a linear function.

x	y
-1	5
0	7
2

a. 5

b. 9

c. 13

d. 11

please select the best answer from the choices provided

a

b

c

d

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points \((-1, 5)\) and \((0, 7)\), we have \(m=\frac{7 - 5}{0 - (-1)}=\frac{2}{1}=2\).

Step2: Find the equation of the line

The slope - intercept form of a line is \(y = mx + b\). We know \(m = 2\) and from the point \((0, 7)\), when \(x = 0\), \(y=b\), so \(b = 7\). The equation of the line is \(y=2x + 7\).

Step3: Find y when x = 2

Substitute \(x = 2\) into the equation \(y=2x + 7\). Then \(y=2\times2+7=4 + 7=11\).

Answer:

d. 11