Question

determine the equation, in slope-intercept form, for the line shown in the graph below:

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, 1), so the y-intercept \( b = 1 \).

Step2: Calculate the slope

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

Step3: Write the equation in slope-intercept form

The slope-intercept form is \( y = mx + b \). Substituting \( m = -1 \) and \( b = 1 \), we get \( y = -x + 1 \).

Answer:

\( y = -x + 1 \)