Question

write the equation of the line in fully simplified 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 \((0,2)\), so \(b = 2\).

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

We can use two points on the line. Let's take \((0,2)\) and \((3,0)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1 = 2,x_2=3,y_2 = 0\) into the formula:
\(m=\frac{0 - 2}{3-0}=\frac{- 2}{3}=-\frac{2}{3}\)

Step4: Write the equation

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

Answer:

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