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 )