Graph each of the following equations by first solving for y.
2x – 3y = 12
so it would be:
y = 2/3x – 4
and the solutions points would be:
So (-3,-6) is a solution
To graph the equation 2x – 3y = 12, you need to first solve for y and rewrite it in the form y = mx + b, where m is the slope and b is the y-intercept.
Given equation: 2x – 3y = 12
To solve for y:
1. Subtract 2x from both sides of the equation: -3y = -2x + 12
2. Divide both sides by -3 to isolate y: y = (2/3)x - 4
Now that you have the equation in the form y = (2/3)x - 4, where the slope is 2/3 and the y-intercept is -4, you can graph it.
To graph the equation:
1. Start by plotting the y-intercept point, which is at (0, -4). This is the point on the y-axis where the line crosses.
2. Use the slope (2/3) to find additional points on the line. The slope indicates that for every increase of 3 in x, there is an increase of 2 in y. Since the slope is positive, you will move up and to the right.
- From the y-intercept point (0, -4), move 3 units to the right and 2 units up. Plot a point at (3, -2).
- Repeat the process to find more points if needed.
Connect the plotted points with a straight line. The resulting line represents the graph of the equation 2x – 3y = 12, or y = (2/3)x - 4.
For the given solution point (-3, -6), you can verify that it lies on the graph of the equation by substituting the values of x and y into the equation:
2(-3) - 3(-6) = 12
-6 + 18 = 12
12 = 12
Since the equation holds true for the given point, (-3, -6) is indeed a solution.