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 \((4,3)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1=-3,x_2 = 4,y_2 = 3\) into the formula:
\(m=\frac{3-(-3)}{4 - 0}=\frac{3 + 3}{4}=\frac{6}{4}=\frac{3}{2}\)

Step4: Write the equation

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

Answer:

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