Question

write the equation of the line in slope-intercept form, $y = mx + b$.

Explanation:

Step1: Find the slope \(m\)

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(0,3)\) (the \(y\) - intercept point) and \((x_2,y_2)=( - 2,0)\). Then \(m=\frac{3-0}{0-( - 2)}=\frac{3}{2}\).

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

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

Step3: Write the equation

Substitute \(m=\frac{3}{2}\) and \(b = 3\) into \(y=mx + b\). The equation is \(y=\frac{3}{2}x+3\).

Answer:

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