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Express the relation below as a set of ordered pairs. $\newline$ Fill in the blank. $\newline$ $(\_,2)$ $\newline$ $(2,17)$ $\newline$ $(16,4)$

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Multiply radical expressions

Full solution

Q. Express the relation below as a set of ordered pairs.

\newline

Fill in the blank.

\newline

(\_,2)

\newline

(2,17)

\newline

(16,4)

Identify Pattern: To find the missing $x$ -value that corresponds to $y=2$ , we need to look for a pattern in the given ordered pairs. The second ordered pair $(2,17)$ suggests that when $x$ is $2$ , $y$ is $17$ .
Analyze Ordered Pairs: Looking at the third ordered pair $(16,4)$ , we can see that when $x$ is $16$ , $y$ is $4$ .
Calculate Slope: We need to find a relationship between $x$ and $y$ . Let's assume the relationship is linear and try to find the slope using the given points $(2,17)$ and $(16,4)$ . The slope ( $m$ ) is calculated by the change in $y$ divided by the change in $x$ , so $m = (4 - 17) / (16 - 2)$ .
Find Slope: Calculating the slope, $m = (4 - 17) / (16 - 2) = -13 / 14$ .
Find Y-Intercept: Now we have the slope, we can use one of the points to find the y-intercept $b$ using the equation $y = mx + b$ . Let's use the point $(2,17)$ . Plugging in the values, we get $17 = \frac{-13}{14} \cdot 2 + b$ .
Solve for Y-Intercept: Solving for $b$ , we get $b = 17 - (-\frac{13}{14})\cdot 2 = 17 + \frac{13}{7} = 17 + 1.857\ldots$
Correct Y-Intercept: Adding $17$ and $1.857$ gives us $b = 18.857\ldots$ However, this should be a simple fraction, not a decimal. Let's correct this. We have $b = 17 + \frac{13}{7} = 17 + 1 \frac{6}{7} = 18 \frac{6}{7}.$

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