Question

the points a(0,5), b(4,2), and c(0,2) form the vertices of a right triangle in the coordinate plane. what is the equation of the line that forms the hypotenuse? the equation of the line is
(type your answer in slope - intercept form.)

Explanation:

Step1: Find the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(A(0,5)\) be \((x_1,y_1)\) and \(B(4,2)\) be \((x_2,y_2)\).
\(m=\frac{2 - 5}{4 - 0}=\frac{-3}{4}=-\frac{3}{4}\)

Step2: Use the slope - intercept form \(y=mx + b\)

We know that the line passes through \(A(0,5)\). Substitute \(x = 0\), \(y = 5\) and \(m=-\frac{3}{4}\) into \(y=mx + b\).
When \(x = 0\), \(y=b\). So \(b = 5\)

Step3: Write the equation

Substitute \(m = -\frac{3}{4}\) and \(b = 5\) into \(y=mx + b\).
The equation is \(y=-\frac{3}{4}x + 5\)

Answer:

\(y = -\frac{3}{4}x + 5\)