Question

a function is represented by the values in the table.

x	y
-2	-4
-1	-1
0	2
1	5

Explanation:

Step1: Calculate the slope

To find the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the first two points \((-3, -7)\) and \((-2, -4)\). Then \( m=\frac{-4 - (-7)}{-2 - (-3)}=\frac{-4 + 7}{-2 + 3}=\frac{3}{1} = 3 \). Let's check with another pair, say \((-2, -4)\) and \((-1, -1)\). \( m=\frac{-1 - (-4)}{-1 - (-2)}=\frac{-1 + 4}{-1 + 2}=\frac{3}{1}=3 \). So the slope is constant (\( m = 3 \)).

Step2: Find the y - intercept

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y=2 \). So \( b = 2 \).

Step3: Write the equation of the line

The equation of a line in slope - intercept form is \( y=mx + b \). Substituting \( m = 3 \) and \( b = 2 \), we get \( y=3x + 2 \).

Answer:

The equation of the function is \( y = 3x+2 \) (If the question was to find the equation of the linear function represented by the table. Since the question was not fully stated, but based on the table of a linear function, the equation is derived as above).