SOLUTION: 3x-6y=9 You have to solve for x and y. Then graph the two points on a graph. Then name the slope and y intercept. Thanks in advance

Algebra ->  Graphs -> SOLUTION: 3x-6y=9 You have to solve for x and y. Then graph the two points on a graph. Then name the slope and y intercept. Thanks in advance      Log On


   

Question 17311: 3x-6y=9 You have to solve for x and y. Then graph the two points on a graph. Then name the slope and y intercept.
Thanks in advance
Found 2 solutions by mmm4444bot, gerleng:
Answer by mmm4444bot(95) About Me  (Show Source):
You can put this solution on YOUR website!
Hi There:
I will show you how to solve the equation for x and y, but it's not necessary if you only need to find the coordinates of two points.
In fact, finding the coordinates of two points does not require solving the equation at all. The two easiest points to find are the x- and y-intercepts.
The x-intercept occurs when y = 0.
The y-intercept occurs when x = 0.
Substitute 0 for y:
3x - 6(0) = 9
3x = 9
x = 3
The x-intercept is at the point (3, 0).
Substitute 0 for x:
3(0) - 6y = 9
-6y = 9
y = -9/6
y = -3/2
The y-intercept is at the point (0, -3/2).
To solve the equation for x means that we want to isolate the variable x on one side of the equals sign and move everything else to the other side.
Start by isolating 3x first; move the -6y term to the other side by adding it to both sides of the equation.
3x - 6y + 6y = 9 + 6y
3x = 9 + 6y
Now we solve for x by dividing both sides by 3.
(3x)/3 = (9 + 6y)/3
x = 9/3 + (6y)/3
x = 3 + 2y
We do something similar to solve the equation for y.
Move the 3x term to the other side to isolate -6y. We do this by subtracting 3x from both sides.
3x - 3x - 6y = 9 - 3x
-6y = 9 - 3x
Divide both sides by -6 to solve for y.
(-6y)/(-6) = (9 - 3x)/(-6)
y = 9/(-6) - (3x)/(-6)
y = -3/2 + x/2
This last equation is usually written like this:
y = (1/2)*x - 3/2
and it is called the slope-intercept form of the equation for the line. It is called this because it shows at a quick glance what the slope is and what the y-intercept is.
It's this form: y = m*x + b
where m is the slope and b is the y-intercept.
y = (1/2)*x - 3/2
Solving the equation for y shows us that m = 1/2 and b = -3/2.
~ Mark

Answer by gerleng(1) About Me  (Show Source):
You can put this solution on YOUR website!
finding the coordinates of two points does not require solving the equation at all. The two easiest points to find are the x- and y-intercepts.
The x-intercept occurs when y = 0.
The y-intercept occurs when x = 0.
Substitute 0 for y:
3x - 6(0) = 9
3x = 9
x = 3
The x-intercept is at the point (3, 0).
Substitute 0 for x:
3(0) - 6y = 9
-6y = 9
y = -9/6
y = -3/2
The y-intercept is at the point (0, -3/2).
To solve the equation for x means that we want to isolate the variable x on one side of the equals sign and move everything else to the other side.
Start by isolating 3x first; move the -6y term to the other side by adding it to both sides of the equation.
3x - 6y + 6y = 9 + 6y
3x = 9 + 6y
Now we solve for x by dividing both sides by 3.
(3x)/3 = (9 + 6y)/3
x = 9/3 + (6y)/3
x = 3 + 2y
We do something similar to solve the equation for y.
Move the 3x term to the other side to isolate -6y. We do this by subtracting 3x from both sides.
3x - 3x - 6y = 9 - 3x
-6y = 9 - 3x
Divide both sides by -6 to solve for y.
(-6y)/(-6) = (9 - 3x)/(-6)
y = 9/(-6) - (3x)/(-6)
y = -3/2 + x/2
This last equation is usually written like this:
y = (1/2)*x - 3/2
and it is called the slope-intercept form of the equation for the line. It is called this because it shows at a quick glance what the slope is and what the y-intercept is.
It's this form: y = m*x + b
where m is the slope and b is the y-intercept.
y = (1/2)*x - 3/2
Solving the equation for y shows us that m = 1/2 and b = -3/2.