Q. answervy=3x+6Problem\begin{tabular}{|c|c|}\hlineX & y \\\hline 1 & 80 \\\hline 2 & 130 \\\hline 3 & 180 \\\hline 4 & 230 \\\hline 5 & 280 \\\hline\end{tabular}What equation represents the linear relationship shown in the table?Mrs. Casias Math 2020 。
Check Linear Pattern: First, let's check if the values in the table follow a linear pattern by finding the difference between the y-values for consecutive x-values.Difference between y when x=2 and x=1: 130−80=50.Difference between y when x=3 and x=2: 180−130=50.Difference between y when x1 and x=3: x3.Difference between y when x5 and x1: x7.Since the difference is constant, it's a linear relationship.
Find Slope: Now, let's use two points from the table to find the slope m of the line.Using points (1,80) and (2,130), the slope m is calculated as:m=x2−x1y2−y1=2−1130−80=150=50.
Use Point-Slope Form: With the slope m=50, we can use the point-slope form to write the equation of the line.Let's use the point (1,80) and the slope m=50.The point-slope form is y−y1=m(x−x1).Plugging in the values, we get y−80=50(x−1).
Simplify Equation: Now, let's simplify the equation to get it into slope-intercept form, y=mx+b.y−80=50x−50.Adding 80 to both sides gives us y=50x+30.
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