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answerv

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 。

answerv\newliney=3x+6 y=3 x+6 \newlineProblem\newline\begin{tabular}{|c|c|}\newline\hlineX X & y y \\\newline\hline 11 & 8080 \\\newline\hline 22 & 130130 \\\newline\hline 33 & 180180 \\\newline\hline 44 & 230230 \\\newline\hline 55 & 280280 \\\newline\hline\newline\end{tabular}\newlineWhat equation represents the linear relationship shown in the table?\newlineMrs. Casias Math 20202020

Full solution

Q. answerv\newliney=3x+6 y=3 x+6 \newlineProblem\newline\begin{tabular}{|c|c|}\newline\hlineX X & y y \\\newline\hline 11 & 8080 \\\newline\hline 22 & 130130 \\\newline\hline 33 & 180180 \\\newline\hline 44 & 230230 \\\newline\hline 55 & 280280 \\\newline\hline\newline\end{tabular}\newlineWhat equation represents the linear relationship shown in the table?\newlineMrs. Casias Math 20202020
  1. Check Linear Pattern: First, let's check if the values in the table follow a linear pattern by finding the difference between the yy-values for consecutive xx-values.\newlineDifference between yy when x=2x=2 and x=1x=1: 13080=50130 - 80 = 50.\newlineDifference between yy when x=3x=3 and x=2x=2: 180130=50180 - 130 = 50.\newlineDifference between yy when xx11 and x=3x=3: xx33.\newlineDifference between yy when xx55 and xx11: xx77.\newlineSince the difference is constant, it's a linear relationship.
  2. Find Slope: Now, let's use two points from the table to find the slope mm of the line.\newlineUsing points (1,80)(1, 80) and (2,130)(2, 130), the slope mm is calculated as:\newlinem=y2y1x2x1=1308021=501=50m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{130 - 80}{2 - 1} = \frac{50}{1} = 50.
  3. Use Point-Slope Form: With the slope m=50m=50, we can use the point-slope form to write the equation of the line.\newlineLet's use the point (1,80)(1, 80) and the slope m=50m=50.\newlineThe point-slope form is yy1=m(xx1)y - y_1 = m(x - x_1).\newlinePlugging in the values, we get y80=50(x1)y - 80 = 50(x - 1).
  4. Simplify Equation: Now, let's simplify the equation to get it into slope-intercept form, y=mx+by = mx + b.\newliney80=50x50y - 80 = 50x - 50.\newlineAdding 8080 to both sides gives us y=50x+30y = 50x + 30.

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