Question

write the equation of the line in fully simplified slope-intercept form.
answer attempt 1 out of 2
answer:

Explanation:

Step1: Identify 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 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 \((3,-4)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1=-2,x_2 = 3,y_2=-4\) into the formula:
\(m=\frac{-4-(-2)}{3 - 0}=\frac{-4 + 2}{3}=\frac{-2}{3}\)

Step4: Write the equation

Substitute \(m =-\frac{2}{3}\) and \(b=-2\) into the slope - intercept form \(y=mx + b\).
We get \(y=-\frac{2}{3}x-2\)

Answer:

\(y =-\frac{2}{3}x-2\)