Question 75806: Determine the Equation of each line
x intercept=4 y interccept = -3
Thanks!
T Found 2 solutions by bucky, venugopalramana:Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! x intercept = 4 & y intercept = -3
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A form of equation that can be used to represent the equation of the line that has a y intercept
of -3 and an x intercept of +4 is the slope intercept form. This form is:
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y = mx + b
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where m is the slope of the line and b is the y intercept.
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The problem tells us that the y intercept is -3. This is half of the information that we
need ... it is the b that we are looking for. When we put this into the equation form it
becomes:
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y = mx - 3
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All we have to do now is find the slope m. We can do this in a couple of different
ways. One of the ways is to make a quick sketch of a coordinate system. Put a dot on
the y-axis at -3. Then go to the x-axis and put a dot at +4. (Those dots represent
the x and y intercepts that are given in the problem.) Start at the dot on the y axis.
Note that you have to go horizontally to the right 4 units to be under the dot on the
x-axis. Also note that you then have to go up 3 units to get to the dot on the x-axis.
That's all the information we need ... +4 to the right and then +3 up to get the dot on the
x-axis. The slope is the vertical change (+3) divided by the horizontal change (+4).
This is 3/4 and we can substitute this for m in the slope intercept equation that we
have so far. This makes the equation:
.
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and that's an equation for the line that has the given intercepts.
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Note that we could also get m (the slope) by identifying the two known points on the line.
The intercept points in coordinate form are the y intercept (0, -3) and the x intercept (4, 0).
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Call (0, -3) the point . The corresponding parts are and . Similarly call (4, 0) the point which means that the
corresponding parts are and . The equation for the slope is:
.
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Just substitute the values that we defined above. When we do, the equation becomes:
.
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This simplifies to
.
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And this is exactly what we found previously. So using this method would also give us
the slope intercept equation:
.
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Hope this gives you some insight into finding an equation for a line that is defined
by two points ... the x and y intercepts.
You can put this solution on YOUR website! Determine the Equation of each line
x intercept=4 y interccept = -3
Thanks!
std eqn. is
X/A + Y/B =1...A=X INTERCEPT....B=Y INTERCEPT
X/4 + Y/-3=1
-3X+4Y=-12
Y=(3X/4)-3
(