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.

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

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

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first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

okay wait before i answer, is this for your points on a graph?