Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

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

The line crosses the y - axis at \((0,-2)\), so \(b=-2\).

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

We can use two points on the line. Let's take \((0, - 2)\) and \((-2,0)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1=-2,x_2=-2,y_2 = 0\) into the formula, we get \(m=\frac{0-(-2)}{-2 - 0}=\frac{2}{-2}=-1\).

Step4: Write the equation

Substitute \(m=-1\) and \(b = - 2\) into \(y=mx + b\). We get \(y=-x-2\).

Answer:

\(y=-x - 2\)