Question

use the graph of the function to complete the table.
input | output
3 | 5
4 |
7 | 9

Explanation:

Step1: Determine the function's equation

The graph is a line. Let's find its slope \( m \) and y - intercept \( b \). The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the graph, when \( x = 0 \), \( y=2 \), so \( b = 2 \).
We can use two points to find the slope. We know the point \( (0,2) \) and from the table, when \( x = 3 \), \( y = 5 \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \( (x_1,y_1)=(0,2) \) and \( (x_2,y_2)=(3,5) \), we get \( m=\frac{5 - 2}{3 - 0}=\frac{3}{3}=1 \). So the equation of the line is \( y=x + 2 \).

Step2: Find the output for \( x = 4 \)

Substitute \( x = 4 \) into the equation \( y=x + 2 \). Then \( y=4 + 2=6 \).
We can also check using the graph. For \( x = 4 \), we move 4 units along the x - axis and then find the corresponding y - value on the line, which should be 6.

Answer:

6