Question

1. using the table below, answer the following questions:

x	y
6	17
8	12
10	7

1. is this a function?
2. if it is a function, find the y-intercept.

Explanation:

Sub - question 1: Is this a function?

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value).

Step2: Check the x - values in the table

The x - values are 4, 6, 8, 10. Each x - value appears only once, and for each x - value, there is exactly one corresponding y - value. So, this relation is a function.

Step1: Determine the type of function (linear in this case)

First, we can find the slope (m) between two points. Let's take the points (4, 22) and (6, 17). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{17 - 22}{6 - 4}=\frac{- 5}{2}=-2.5$.

Step2: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m(x - x_1)$. Using the point (4, 22) and $m=-2.5$, we have $y - 22=-2.5(x - 4)$.

Step3: Simplify the equation to slope - intercept form ($y = mx + b$, where b is the y - intercept)

$y-22=-2.5x + 10$. Then, $y=-2.5x+10 + 22=-2.5x + 32$.
We can also verify with another point. Let's take (6, 17). Substitute x = 6 into $y=-2.5x + 32$: $y=-2.5\times6+32=-15 + 32 = 17$, which matches.
For the y - intercept, we set x = 0 in the equation $y=-2.5x + 32$. When x = 0, $y = 32$.

Answer:

Yes

Sub - question 2: If it is a function, find the y - intercept.