Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 1)\) and \((6, 0)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, 1)\) (\(x_1 = 0, y_1 = 1\)) and \((6, 0)\) (\(x_2 = 6, y_2 = 0\)):
\(m=\frac{0 - 1}{6 - 0}=\frac{-1}{6}=-\frac{1}{6}\)

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0, 1)\), we can see that \(b = 1\).

Step4: Write the equation in slope - intercept form (\(y=mx + b\))

Substitute \(m = -\frac{1}{6}\) and \(b = 1\) into the slope - intercept form:
\(y=-\frac{1}{6}x + 1\)

Answer:

\(y = -\frac{1}{6}x + 1\)