Question

1. Calculate the slope of the line between the two distinct points that create the hypotenuse for each of the three triangles shown in the figure. Show work.
2. Write an equation for the line.

Answer 1

Calculate the equation for the line: y = mx + b

First, find the slope. Find two points, and use point-slope formula:

m = slope = (y₂ - y₁)/(x₂ - x₁)

Let (x₁ , y₁) = (0 , 0) & (x₂ , y₂) = (9, 6)

slope = (9 - 0)/(6 - 0) = 9/6

Plug in 9/6 (or a simplified version) for m

y = (3/2)x + b

Now, solve for b. Get a coordinate point to use in the equation. In this case, use (6, 4), in which x = 6, y = 4

4 = (3/2)(6) + b

Simplify.

4 = (3 x 6)/2 + b

4 = 3 x 3 + b

4 = 9 + b

Isolate the b. Note the equal sign, what you do to one side, you do to the other. Subtract 9 from both sides

4 (-9) = 9 (-9) + b

b = 4 - 9

b = -5

Plug in -5 for b

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y = (3/2)x - 5 is your equation (2.); 3/2 is your slope (1.)

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