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:

Solution

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 \(\boxed{-4}\).

From Solvely APP
Source: https://solvelyapp.com/problems/VzVfITAqWb/

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