Step 1: Write out the formula for the equation of a line between two points (x1,y1) and (x2,y2):
The equation of a line passing through points (x1,y1) and (x2,y2) is given by:
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}_{}[/tex]
Step 2: Write out the coordinates of two points on the given line.
From the graph, we can see that two points on the line are given by:
[tex](0,3)\text{ and }(3,1)[/tex]
In this case,
[tex]\begin{gathered} x_1=0 \\ y_1=3 \\ x_2=3 \\ y_2=1 \end{gathered}[/tex]
Step 3: Substitute the values into the formula to find the equation of the line:
[tex]\begin{gathered} \frac{y-3}{1-3}=\frac{x-0}{3-0} \\ \text{Subtracting the numbers, we have:} \\ \frac{y-3}{-2}=\frac{x}{3} \\ \text{Cross-multiplying, we have:} \\ 3(y-3)=-2x \\ \text{Expanding the left side, we have:} \\ 3y-9=-2x \\ \text{Adding 9 to both sides, we have} \\ 3y=-2x+9 \end{gathered}[/tex]
Hence,
[tex]y=\frac{-2x+9}{3}[/tex]
Therefore, the function rule is given by:
y = (-2x + 9)/3
