Question

write the equation that models the linear relationship.
the equation \boxed{} models the linear relationship.
(use integers or fractions for any numbers in the equation)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 3)\) (the y - intercept) and \((6, 5)\) (we can also use other points, but these are easy to identify).

Step2: Calculate the slope (\(m\))

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(6,5)\). Then \(m=\frac{5 - 3}{6 - 0}=\frac{2}{6}=\frac{1}{3}\).

Step3: Use the slope - intercept form (\(y=mx + b\))

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=\frac{1}{3}\) and from the point \((0,3)\), \(b = 3\). So the equation of the line is \(y=\frac{1}{3}x+3\).

Answer:

\(y = \frac{1}{3}x + 3\)