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 (\( m \))

Use two points, e.g., \( (0, 2) \) and \( (2, 0) \). Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{2 - 0} = \frac{-2}{2} = -1 \).

Step4: Write the equation

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

Answer:

\( y = -x + 2 \)