Question

write the equation of the line in fully simplified slope - intercept form.
(there is a coordinate grid with a line plotted on it. the x - axis ranges from - 12 to 12, and the y - axis ranges from - 12 to 12. the line passes through some grid points. there is also an answer section with attempt 2 out of 2 and a submit answer button.)

Explanation:

Step1: Identify slope-intercept form

Slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

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

The line crosses the y-axis at \( (0, -3) \), so \( b = -3 \).

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

Use two points, e.g., \( (0, -3) \) and \( (3, 0) \).
Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
Substitute: \( m = \frac{0 - (-3)}{3 - 0} = \frac{3}{3} = 1 \).

Step4: Write the equation

Substitute \( m = 1 \) and \( b = -3 \) into \( y = mx + b \):
\( y = 1x - 3 \) or \( y = x - 3 \).

Answer:

\( y = x - 3 \)