Question

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

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept (\(b\))

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at \((0,- 1)\), so \(b=-1\).

Step3: Calculate the slope (\(m\))

We can use two points on the line to calculate the slope. Let's use the points \((0,-1)\) and \((1, - 2)\). The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1=-1,x_2 = 1,y_2=-2\) into the formula:
\(m=\frac{-2-(-1)}{1 - 0}=\frac{-2 + 1}{1}=\frac{-1}{1}=-1\)

Step4: Write the equation

Substitute \(m=-1\) and \(b = - 1\) into the slope - intercept form \(y=mx + b\).
We get \(y=-x-1\)

Answer:

\(y=-x - 1\)