Question

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

Explanation:

Step1: Identify slope-intercept form

The slope - intercept form of a line 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 \((0,5)\), so \(b = 5\).

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

We can use two points on the line. Let's take \((0,5)\) and \((2,0)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1 = 5,x_2 = 2,y_2 = 0\) into the formula: \(m=\frac{0 - 5}{2 - 0}=\frac{- 5}{2}=-2.5\) or \(m =-\frac{5}{2}\).

Step4: Write the equation

Substitute \(m =-\frac{5}{2}\) and \(b = 5\) into the slope - intercept form \(y=mx + b\).
We get \(y=-\frac{5}{2}x + 5\).

Answer:

\(y =-\frac{5}{2}x + 5\)