SOLUTION: This is from a worksheet. Find the y-intercept of the graph of the equation 5x + 3y -15 = 0. State your answer as an ordered pair. I do not understand how to do this.

Question 89147: This is from a worksheet.
Find the y-intercept of the graph of the equation 5x + 3y -15 = 0. State your answer as an ordered pair.
I do not understand how to do this.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
5x + 3y -15 = 0
.
You are asked to find the y-intercept and to put the answer in the form of an ordered pair.
.
Let's begin by defining a couple of the terms just to make sure that we know what we are
trying to do.
.
The y-intercept is the point on the y-axis where the graph crosses.
.
An ordered pair is the way you identify a point on the coordinate system. Each point on
the coordinate system is identified by an x value and a y value. The convention is to write
ordered pairs in the form (x, y) where x is the position of the point in the x direction
and the corresponding y is the position of the point in the y direction. As an example,
the point (2, -3) is located by going to +2 on the x-axis and drawing a vertical line through
the +2. Then going to -3 on the y-axis and drawing a horizontal line through that point.
The point specified by the ordered pair (2, -3) is located where the vertical and horizontal
lines cross.
.
Perhaps you knew these two definitions already.
.
We can now extend on these definitions to solve the problem. Think about a point on the
y-axis. What would be the x value of such a point. The vertical line along the y-axis corresponds
to an x-value of 0 ... (think "go to the point x equals zero and drawing a vertical
line through that point.
.
So that tells you that in the given equation, you can set x equal to zero and find the
corresponding value of y by solving for y.
.
The given equation is:
.
5x + 3y -15 = 0
.
Substitute 0 for x to get:
.
5(0) + 3y - 15 = 0
.
Notice that the term 5(0) is zero, so it disappears. Then the equation becomes
.
3y -15 = 0
Solve this equation by adding 15 to both sides to get:
.
3y = 15
.
Finally, solve for y by dividing both sides by 3 and you have
.
y = 5
.
Now you know that when x = 0, then y = 5. So the ordered pair that identifies the y-intercept
is:
.
(0, 5)
.
Just for �fun�, what would the ordered pair be for the x-intercept? By using the same
logical thinking that we did for the y-axis intercept, you can see that a point on the x-axis
will have y equal to zero, because that must be the value of y for the horizontal
line to go down the x-axis.
.
Now you can return to the given equation and set y equal to zero so that you can solve for
the corresponding value of x on the x-axis:
.
5x + 3(0) -15 = 0
.
But 3(0) equals zero so that term disappears and you are left with
.
5x � 15 = 0
.
Solve by adding 15 to both sides to get:
.
5x = 15
.
Finally, divide both sides by 5 to get that:
.
x = 3
.
So the ordered pair for the x-intercept is (3, 0)
.
Once you understand the basic concept you will be able to solve problems such as these much
faster. You will learn to say to yourself, �I can find the y-intercept by setting x = 0
and solving for y.� The ordered pair for the y-intercept will then be (0, y) where y is
the value you find when x equals zero.
.
Similarly, you will say, �I can find the x-intercept by setting y = 0 and solving the
equation for x.� The ordered pair for the x-intercept will then be (x, 0) where x is the
value you find from the equation by setting y equal to zero.
.
Hope this clears up the situation for you. And in summary, the answer to your problem is
(0, 5)

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