Sure! I'd be happy to help you with that. To draw the graph of the equation 3x + 2y = 12, we need to rearrange it into the slope-intercept form, which is y = mx + b. In this form, we can easily identify the slope and y-intercept.
Let's rearrange the equation:
3x + 2y = 12
2y = -3x + 12
y = (-3/2)x + 6
Now we have the equation in slope-intercept form, where the slope is -3/2 and the y-intercept is 6. To graph this equation, we can start by plotting the y-intercept at the point (0, 6).
Next, we can use the slope to find additional points on the graph. The slope of -3/2 means that for every 2 units we move to the right on the x-axis, we need to move 3 units down on the y-axis. So, starting from the y-intercept point (0, 6), we can move 2 units to the right and 3 units down to get to the next point.
Using this process, we can continue drawing more points and then connect them to create the graph of the equation. It should look like a straight line with a negative slope.
Now, let's determine whether the point (x=2, y=3) is a solution of the equation. To do this, we can simply check if substituting x=2 and y=3 into the original equation makes it true.
3x + 2y = 12
3(2) + 2(3) = 12
6 + 6 = 12
12 = 12
Since both sides of the equation are equal, we can conclude that (x=2, y=3) is indeed a solution of the equation.
I hope this helps! Let me know if you have any further questions.
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Answer:
Sure! I'd be happy to help you with that. To draw the graph of the equation 3x + 2y = 12, we need to rearrange it into the slope-intercept form, which is y = mx + b. In this form, we can easily identify the slope and y-intercept.
Let's rearrange the equation:
3x + 2y = 12
2y = -3x + 12
y = (-3/2)x + 6
Now we have the equation in slope-intercept form, where the slope is -3/2 and the y-intercept is 6. To graph this equation, we can start by plotting the y-intercept at the point (0, 6).
Next, we can use the slope to find additional points on the graph. The slope of -3/2 means that for every 2 units we move to the right on the x-axis, we need to move 3 units down on the y-axis. So, starting from the y-intercept point (0, 6), we can move 2 units to the right and 3 units down to get to the next point.
Using this process, we can continue drawing more points and then connect them to create the graph of the equation. It should look like a straight line with a negative slope.
Now, let's determine whether the point (x=2, y=3) is a solution of the equation. To do this, we can simply check if substituting x=2 and y=3 into the original equation makes it true.
3x + 2y = 12
3(2) + 2(3) = 12
6 + 6 = 12
12 = 12
Since both sides of the equation are equal, we can conclude that (x=2, y=3) is indeed a solution of the equation.
I hope this helps! Let me know if you have any further questions.
Step-by-step explanation:
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