Q. Graph this function: \( y = x + 2 \). Click to select points on the graph.

Graphing the function: \(y = x + 2\)

1. Recognize the form and identify slope and intercept.The equation is in slope-intercept form \(y = mx + b\), so compare to get:

   Slope: \(m = 1\).

   y-intercept: \(b = 2\), which corresponds to the point \((0,2)\) where the line crosses the y-axis.

   Interpretation of slope: a slope of \(1\) means that for each increase of 1 in x the value of y increases by 1 (rise of 1 for a run of 1).

2. Choose convenient x-values and compute corresponding y-values.Pick easy x-values (for example: \(-2,-1,0,1,2\)) and use the rule \(y = x + 2\) to get y:
   

   x	Compute y = x + 2	Point (x,y)
   \(-2\)	\(y = -2 + 2 = 0\)	\((-2,\,0)\)
   \(-1\)	\(y = -1 + 2 = 1\)	\((-1,\,1)\)
   \(0\)	\(y = 0 + 2 = 2\)	\((0,\,2)\)
   \(1\)	\(y = 1 + 2 = 3\)	\((1,\,3)\)
   \(2\)	\(y = 2 + 2 = 4\)	\((2,\,4)\)

3. Plot the points on the coordinate plane.On your graph or graphing tool:
   1. Draw and label the x-axis and y-axis and choose an appropriate scale (one unit per tick mark is simplest).
   2. Mark and label each of the computed points: \((-2,0),\,(-1,1),\,(0,2),\,(1,3),\,(2,4).
   3. Any two distinct plotted points are sufficient to determine the line. For clarity plot at least three points to confirm they are collinear.
4. Draw the line through the plotted points.Since this is a linear equation, all plotted points lie on one straight line. Use a ruler or the line tool in your graphing program to connect the points and extend the line across the graph in both directions. The line will pass through the y-intercept \((0,2)\) and rise one unit for every one unit moved to the right.
5. Points to click (select) on the graph.Select any of these points to define or test the line. Recommended points to click:
   • \((0,\,2)\)
   • \((1,\,3)\)
   • \((-2,\,0)\)
   • \((2,\,4)\)
   • \((-1,\,1)\)

   Click any two of the above points to plot the line; clicking more points will verify correctness.

6. Final description of the graph.The graph of \(y = x + 2\) is a straight line with slope \(1\) and y-intercept \(2\). Its points satisfy \(y – 2 = 1\cdot x\), so the line passes through the listed points and continues infinitely in both directions.