Question

two 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 square (type your answer in slope - intercept form)

Explanation:

Step1: Calculate the slope \(m\)

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

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

We know \(m =-\frac{3}{4}\) and when \(x = 0\), \(y = 5\) (from the point \(A(0,5)\)), so \(b = 5\).

Step3: Write the equation

Substitute \(m\) and \(b\) into \(y=mx + b\), we get \(y=-\frac{3}{4}x + 5\).

Answer:

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