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answer

y=3x+6
Problem

X

Y

1
80

2
130

3
180

4
230

5
280

What equation represents the linear relationship shown in the table?
Mrs. Casias Math 2020
*

answer $\newline$ $y=3 x+6$ $\newline$ Problem $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline $X$ & $Y$ \\ $\newline$ \hline $1$ & $80$ \\ $\newline$ \hline $2$ & $130$ \\ $\newline$ \hline $3$ & $180$ \\ $\newline$ \hline $4$ & $230$ \\ $\newline$ \hline $5$ & $280$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ What equation represents the linear relationship shown in the table? $\newline$ Mrs. Casias Math $2020$ $\cdot$

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Solve word problems by finding two-variable equations

Full solution

Q. answer

\newline

y=3 x+6

\newline

Problem

\newline

\begin{tabular}{|c|c|}

\newline

\hline

X

&

Y

\\

\newline

\hline

1

&

80

\\

\newline

\hline

2

&

130

\\

\newline

\hline

3

&

180

\\

\newline

\hline

4

&

230

\\

\newline

\hline

5

&

280

\\

\newline

\hline

\newline

\end{tabular}

\newline

What equation represents the linear relationship shown in the table?

\newline

Mrs. Casias Math

2020

\cdot

Calculate y differences: First, let's look at the differences in $y$ when $x$ increases by $1$ . From $x=1$ to $x=2$ , $y$ increases by $50$ ( $130-80$ ). From $x=2$ to $x=3$ , $y$ increases by $50$ ( $x$ $2$ ). This pattern continues for all $x$ values in the table.
Identify linear relationship: Since the increase in $y$ is consistent as $x$ increases, the relationship is linear and the slope ( $m$ ) is $50$ .
Find y-intercept: Now, let's find the y-intercept $b$ by looking at the table. $\newline$ When $x=1$ , $y=80$ . $\newline$ Using the slope we found, we can write the equation as $y=mx+b$ and plug in $x=1$ , $y=80$ , and $m=50$ . $\newline$ $80 = 50(1) + b$
Solve for b: Solving for b, we get $b = 80 - 50$ . $\newline$ $b = 30$
Final equation: So the equation of the line is $y = 50x + 30$ .

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\newline

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\newline

1

\newline

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\newline

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\newline

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\newline

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