Graph the following equation :
2x-3y=-6
type in the equation at
wolframalpha.com
2x=-6 gives you the x intercept
-3x=-6 gives you the y intercept
To graph the equation 2x - 3y = -6, we can start by rearranging the equation to solve for y.
2x - 3y = -6
Subtract 2x from both sides:
-3y = -2x - 6
Divide through by -3:
y = (2/3)x + 2
Now we have the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope is 2/3 and the y-intercept is 2.
To plot the graph, we can start by plotting the y-intercept, which is (0, 2). From there, we use the slope to find additional points on the line.
The slope of 2/3 means that for every increase of 2 in the x-coordinate, the y-coordinate increases by 3. Similarly, for every decrease of 2 in the x-coordinate, the y-coordinate decreases by 3.
Using this information, we can plot two more points on the line. For example, if we move 2 units to the right from the y-intercept (0, 2), we get (2, 3). Similarly, if we move 2 units to the left from the y-intercept, we get (-2, 1).
After plotting multiple points, we can draw a straight line connecting all the points. This line represents the graph of the equation 2x - 3y = -6.