Question

write the equation of this line in slope-intercept 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 \((0,-4)\), so \(b=-4\).

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

We can use two points on the line. Let's take \((0, - 4)\) and \((2,-8)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1=-4,x_2 = 2,y_2=-8\) into the formula: \(m=\frac{-8-(-4)}{2 - 0}=\frac{-8 + 4}{2}=\frac{-4}{2}=-2\).

Step4: Write the equation

Substitute \(m=-2\) and \(b = - 4\) into \(y=mx + b\). We get \(y=-2x-4\).

Answer:

\(y=-2x - 4\)