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 \( (0, 4) \), so \( b = 4 \).

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

Use two points, e.g., \( (0, 4) \) and \( (4, 3) \). Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{4 - 0} = \frac{-1}{4} = -\frac{1}{4} \).

Step4: Write the equation

Substitute \( m = -\frac{1}{4} \) and \( b = 4 \) into \( y = mx + b \): \( y = -\frac{1}{4}x + 4 \).

Answer:

\( y = -\frac{1}{4}x + 4 \)