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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:
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5x + 3y -15 = 0
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You are asked to find the y-intercept and to put the answer in the form of an ordered pair.
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Let's begin by defining a couple of the terms just to make sure that we know what we are
trying to do.
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The y-intercept is the point on the y-axis where the graph crosses.
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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.
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Perhaps you knew these two definitions already.
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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.
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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.
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The given equation is:
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5x + 3y -15 = 0
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Substitute 0 for x to get:
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5(0) + 3y - 15 = 0
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Notice that the term 5(0) is zero, so it disappears. Then the equation becomes
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3y -15 = 0
Solve this equation by adding 15 to both sides to get:
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3y = 15
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Finally, solve for y by dividing both sides by 3 and you have
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y = 5
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Now you know that when x = 0, then y = 5. So the ordered pair that identifies the y-intercept
is:
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(0, 5)
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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.
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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:
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5x + 3(0) -15 = 0
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But 3(0) equals zero so that term disappears and you are left with
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5x – 15 = 0
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Solve by adding 15 to both sides to get:
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5x = 15
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Finally, divide both sides by 5 to get that:
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x = 3
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So the ordered pair for the x-intercept is (3, 0)
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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.
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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.
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Hope this clears up the situation for you. And in summary, the answer to your problem is
(0, 5)
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