Question

to add further points: if you wish to add additional points to your graph, click your graph and select (note that this button toggles between add and stop adding points). then you can add points by clicking in the drawing area as before. to delete a selected point or graph, click. to delete using your keyboard, press delete after selecting a point or selecting a graph. to change the graph label for the active graph, select the desired label from the drop - down menu below \label\. to clear your current graph from the drawing area (restart), select. there is a brief tips tour that summarizes the above information, which you can launch by selecting. for further help with graphing, select. part a create a graph of $y = 2x - 6$. construct a graph corresponding to the linear equation $y = 2x - 6$. view available hint(s) select the elements from the list and add them to the canvas setting the appropriate attributes. press tab to get main menu.

Explanation:

Step1: Find the y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=2x - 6\), when \(x = 0\), we substitute \(x = 0\) into the equation:
\(y=2(0)-6=- 6\). So one point on the line is \((0,-6)\).

Step2: Find another point using the slope

The slope \(m = 2=\frac{2}{1}\), which means for a run of \(1\) (increase in \(x\) by \(1\)), the rise is \(2\) (increase in \(y\) by \(2\)). Starting from the point \((0,-6)\), if we increase \(x\) by \(1\) (so \(x=0 + 1=1\)) and increase \(y\) by \(2\) (so \(y=-6 + 2=-4\)), we get the point \((1,-4)\). We can also use \(x = 3\), then \(y=2(3)-6=6 - 6=0\), so the point \((3,0)\) is also on the line.

Step3: Plot the points and draw the line

Plot the points \((0,-6)\) and \((3,0)\) (or other points we found) on the coordinate plane and then draw a straight line passing through these points.

To create the graph:

1. Locate the point \((0,-6)\) on the y - axis (since \(x = 0\), we move down 6 units from the origin on the y - axis).
2. Locate the point \((3,0)\) on the x - axis (since \(y = 0\), we move 3 units to the right from the origin on the x - axis).
3. Use a straight - edge to draw a line connecting these two points. The line will extend infinitely in both directions.

Answer:

To graph \(y = 2x-6\), plot the points \((0,-6)\) (y - intercept) and \((3,0)\) (x - intercept) and draw a straight line through them. The line has a slope of \(2\) and a y - intercept of \(-6\).