Question

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 \((0, 6)\) and \((6, 0)\) (we can also use other points, but these are easy to identify).

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

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

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,6)\), we can see that \(b = 6\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-1\) and \(b = 6\) into the formula, we get \(y=-x + 6\).

Answer:

\(y=-x + 6\)