Question

what is the linear equation of the graph?
options:
y = -2x -6
y = -3/6x -6
y = 2x -6
y = -6x -2

Explanation:

Step1: Identify the y-intercept

The graph crosses the y-axis at (0, -6), so the y-intercept \( b = -6 \). The slope-intercept form is \( y = mx + b \), so the equation will have \( -6 \) as the constant term.

Step2: Determine the slope

Looking at the graph, we can find two points. Let's take (0, -6) and another point, say (-3, 0) (by observing the grid). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-6)}{-3 - 0} = \frac{6}{-3} = -2 \).

Step3: Form the equation

Using \( m = -2 \) and \( b = -6 \) in \( y = mx + b \), we get \( y = -2x - 6 \).

Answer:

y = -2x - 6 (corresponding to the yellow option: y = -2x -6)