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:
.
y = mx + b
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where m is the slope of the line and b is the y intercept.
.
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:
.
.
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).
.
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:
.
.
Just substitute the values that we defined above. When we do, the equation becomes:
.
.
This simplifies to
.
.
And this is exactly what we found previously. So using this method would also give us
the slope intercept equation:
.
.
Hope this gives you some insight into finding an equation for a line that is defined
by two points ... the x and y intercepts.
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