Question

14 write the slope intercept form of the equation of the line. equation:

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Step2: Find the y-intercept (\( b \))

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

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

Use two points on the line, e.g., \( (0, -1) \) and \( (2, -2) \). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Substituting values: \( m = \frac{-2 - (-1)}{2 - 0} = \frac{-1}{2} = -\frac{1}{2} \).

Step4: Write the equation

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

Answer:

\( y = -\frac{1}{2}x - 1 \)