Question

write the equation of the line in fully simplified slope-intercept form.

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 (\( m \))

We can use two points on the line. Let's take \( (0, - 3) \) and \( (2,0) \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substituting \( x_1 = 0,y_1=-3,x_2 = 2,y_2 = 0 \) into the formula:
\( m=\frac{0-(-3)}{2 - 0}=\frac{3}{2} \)

Step4: Write the equation

Substitute \( m = \frac{3}{2} \) and \( b=-3 \) into \( y=mx + b \):
\( y=\frac{3}{2}x-3 \)

Answer:

\( y=\frac{3}{2}x - 3 \)