Question

for the table, make a scatter plot of the data. draw a trend line, and write its equation.
the equation of the trend line is
(simplify your answer. type an equation. type your answer in slope - intercept form. use integers or decimals for any numbers in the equation )

Explanation:

Step1: Identify Data Points

The data points from the table are \((1,3)\), \((2,5)\), \((3,7)\), \((3,8)\), \((5,10)\), \((6,12)\). Plotting these, we see a positive linear trend.

Step2: Choose Two Points for Trend Line

Let's pick \((1,3)\) and \((6,12)\). Calculate the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{12 - 3}{6 - 1}=\frac{9}{5}=1.8\).

Step3: Find y - intercept (b)

Using point - slope form \(y - y_1=m(x - x_1)\) with \((1,3)\) and \(m = 1.8\):
\(y-3=1.8(x - 1)\)
\(y-3=1.8x-1.8\)
\(y=1.8x + 1.2\) (or using two - point formula, we can also estimate. Another way: using \((2,5)\) and \(m = 2\) (approximate, since the data is roughly linear with slope close to 2). Let's re - calculate with \((1,3)\) and slope \(m = 2\): \(y-3=2(x - 1)\Rightarrow y=2x + 1\). Wait, let's check with the points. For \(x = 1\), \(y=3\): \(2(1)+1 = 3\), good. \(x = 2\), \(y = 5\): \(2(2)+1=5\), good. \(x = 6\), \(y=13\) (close to 12). So the trend line equation is approximately \(y = 2x+1\) (or more accurately, using the two points \((1,3)\) and \((5,10)\): \(m=\frac{10 - 3}{5 - 1}=\frac{7}{4}=1.75\), \(y-3 = 1.75(x - 1)\), \(y=1.75x+1.25\). But the most approximate linear trend with integer coefficients: let's see the pattern. When \(x\) increases by 1, \(y\) increases by 2 (approx). So the equation of the trend line is \(y = 2x + 1\) (or \(y=1.8x + 1.2\), but a simpler integer - based trend line is \(y = 2x+1\)).

Answer:

\(y = 2x + 1\) (or a more precise \(y=1.8x + 1.2\))