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 slope and \( b \) is 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 \( (5, 3) \). Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 2}{5 - 0} = \frac{1}{5} \).

Step4: Write the equation

Substitute \( m = \frac{1}{5} \) and \( b = 2 \) into \( y = mx + b \): \( y = \frac{1}{5}x + 2 \).

Answer:

\( y = \frac{1}{5}x + 2 \)