Question

write an equation in slope - intercept form of the line. (use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Identify two points on the line

Let's assume two points \((x_1,y_1)\) and \((x_2,y_2)\) from the graph. For example, if we take two clear - cut points on the line. Suppose \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(6,1)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values, we get \(m=\frac{1 - 3}{6-0}=\frac{-2}{6}=-\frac{1}{3}\).

Step3: Identify the \(y\) - intercept \(b\)

The \(y\) - intercept is the \(y\) - value when \(x = 0\). From the point \((0,3)\), we have \(b = 3\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-\frac{1}{3}\) and \(b = 3\), we get \(y=-\frac{1}{3}x+3\).

Answer:

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