Problem

2.
\begin{tabular}{|c|c|}
\hline$x$ & $y$ \\
\hline-3 & 5 \\
-2 & 2 \\
-1 & -1 \\
0 & -4 \\
1 & -7 \\
\hline
\end{tabular}
\[
m=
\]
$y$-intercept:

Answer

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Answer

Final Answer: The slope of the line is \(\boxed{-3.0}\) and the y-intercept is \(\boxed{-4}\).

Steps

Step 1 :The problem is asking for the slope (m) of the line that passes through the points given in the table and the y-intercept of the line. The slope of a line can be calculated using the formula \(m = \frac{{y2 - y1}}{{x2 - x1}}\), where \((x1, y1)\) and \((x2, y2)\) are any two points on the line. The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which is when x = 0.

Step 2 :We can use the points (-3, 5) and (-2, 2) to calculate the slope, and the point (0, -4) gives us the y-intercept directly.

Step 3 :Calculating the slope: \(m = \frac{{2 - 5}}{{-2 - (-3)}} = -3.0\)

Step 4 :The y-intercept is the y-coordinate when x = 0, so the y-intercept is -4.

Step 5 :Final Answer: The slope of the line is \(\boxed{-3.0}\) and the y-intercept is \(\boxed{-4}\).

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