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 \((1, - 2)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1 = 2,x_2 = 1,y_2=-2\) into the formula: \(m=\frac{-2 - 2}{1 - 0}=\frac{-4}{1}=-4\).

Step4: Write the equation

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

Answer:

\(y=-4x + 2\)