Question

write the equation of the line, in standard form, with the given information:

Explanation:

Step1: Find two points on the line

From the graph, two points on the line are \((- 6,0)\) and \((0,-6)\)

Step2: Calculate the slope \(m\)

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

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

We know \(m=-1\) and using the point \((0,-6)\), when \(x = 0\), \(y=-6\), so \(b=-6\). The equation in slope - intercept form is \(y=-x - 6\)

Step4: Convert to standard form \(Ax+By = C\)

Add \(x\) to both sides of \(y=-x - 6\). We get \(x + y=-6\)

Answer:

\(x + y=-6\)