Let's solve this problem step by step.

Problem:

We need to find the equation of the line forming the hypotenuse of the right triangle in slope-intercept form ($y = mx + b$).

Given Points:

• $A(0, 5)$
• $B(4, 2)$
• $C(0, 2)$

The hypotenuse is the line connecting A(0, 5) and B(4, 2).

Step 1: Find the slope of the line ($m$).

The formula for slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates of $A(0, 5)$ and $B(4, 2)$: $m = \frac{2 - 5}{4 - 0} = \frac{-3}{4}$

So, the slope ($m$) of the line is: $m = -\frac{3}{4}$

Step 2: Find the y-intercept ($b$).

The slope-intercept form of a line is: $y = mx + b$

Substitute $m = -\frac{3}{4}$ and use one of the given points, $A(0, 5)$, to find $b$. At $A(0, 5)$, $x = 0$ and $y = 5$: $5 = -\frac{3}{4}(0) + b$ $b = 5$

Step 3: Write the equation of the line.

Substitute $m = -\frac{3}{4}$ and $b = 5$ into the slope-intercept form: $y = -\frac{3}{4}x + 5$

Final Answer:

The equation of the line forming the hypotenuse is: $y = -\frac{3}{4}x + 5$

Do you want me to explain any step in more detail? Let me know!

Related Questions:

1. How do you verify if the triangle is a right triangle using slopes?
2. What is the distance of the hypotenuse using the distance formula?
3. How would the equation change if one of the points shifted location?
4. What is the area of the triangle based on the given points?
5. How can you find the perpendicular slope to the hypotenuse?

Tip:

When solving for the slope of a line, always double-check the numerator and denominator to avoid sign errors!