Question

Select all possible numbers that when replaced "?" with the app in the set of ordered pairs {{3,4), (-2,-5),(?,0)} would create a function. .

Answer 1

(3,4) , (-2, -5) , (?, 0)

First pick the first two coordinate to create a function.

`\begin{gathered} (y-y_1)/(x-x_1)\text{ = }(y_2-y_1)/(x_2-x_1) \\ \frac{y\text{ - 4}}{x\text{ - 3}}\text{ = }\frac{-5\text{ - 4}}{-2\text{ - }3} \\ \frac{\text{y - 4}}{x\text{ - 3}}\text{ = }(-9)/(-5) \\ \frac{y\text{ - 4}}{x\text{ - 3}}\text{ = }(9)/(5) \\ \text{Cross multiple} \\ 5(y\text{ - 4) = 9(x - 3)} \\ 5y\text{ - 20 = 9x - }27 \\ 5y\text{ = 9x - 27 + }20 \\ 5y\text{ = 9}x\text{ - }7 \end{gathered}`

Let ? = n

for y = 0,

5(0) = 9x - 7

0 = 9x - 7

9x = 7

x = 7/9

? = 7/9