SOLUTION: A line passes through the point P(-2,3) and has a slope of -1/2. What graph best represents the line?

Question 92683: A line passes through the point P(-2,3) and has a slope of -1/2. What graph best represents the line?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
There are several ways you can do this problem. One way is to use the equation that says
the slope m is equal to:
.

.
where comes from the point P and is +3 and also comes from the point P
and is -2. The problem also tells you that the slope is .
Substituting
these values into the slope equation to get:
.

.
This simplifies to:
.

.
and this is an equation that can be used to graphically represent the line that has a slope
of and have as one point (-2,3). You can find other points on that will be on
the graph by assigning values to x and computing the corresponding values of y. For example,
you can let x = 2. Substitute +2 for x and the equation becomes:
.

.
When you combine the 2+2 to get 4 in the denominator of the right side the equation
becomes:
.

.
If you multiply both sides by 4 the equation becomes:
.

.
On the left side the produce of 4*(-1/2) = -2 and on the right side the 4 in the numerator
cancels with the 4 in the denominator and you are left with just y-3. So the equation now
is:
.

.
You can solve for y by adding +3 to both sides to get:
.

.
So now you know that the point in which x equals 2 and y equals 1 is also on the graph.
.
So now you know two points on the line ... (-2,3) which was given in the problem and (2, 1)
which you just calculated. You can plot these two points and get the graph by drawing a
straight line that goes through these two points.
.
Another way that you could get an equation for that line is to use the slope intercept form
of an equation. The slope intercept form is:
.

.
in which m is the slope and is given as . b is the value of y where the graph
crosses the y-axis. Substituting the value of the slope into this slope
intercept form
results in:
.

.
You are given that the point (-2,3) is on the line. So you can substitute 3 for y and -2 for
x into the equation to get:
.

.
Doing the multiplication on the right side transforms the equation to:
.

.
You can now solve for b by subtracting 1 from both sides to get:
.

.
Now you can substitute this value for b and the slope value of into the slope
intercept form to get another equation for the graph:
.

.
This is the same equation as that we got before. It's just in
a little different form. You can also get more points on the graph from the slope intercept
form by assigning values to x and computing the corresponding value of y. Each time you do
this you get another point on the graph. You can plot these points and connect them with
a line that is then the graph you are looking for.
.
When you get done you should have a graph that looks like this:
.

.
Note that the graph crosses the y axis at +2, which is the value we found for b above.
Also notice that the point (-2,3) is on the graph. Also notice that the slope of the graph
is negative because it slopes down as you move to the right.
.
Hope this helps you to understand the problem a little better.
RELATED QUESTIONS
Which equation represents a line that has a slope of -1 and passes through the point (-2, (answered by josgarithmetic)

graph the line that passes through the point (-1,4) and has a slope of... (answered by kingme18)

what isthe equation of the vertical line that passes through the point (-2, -1).... (answered by ewatrrr)

I need help graphing this - A line passes through the point P (-2,3) and has the slope... (answered by stanbon)

Oscar wants to write an equation of a line that passes through the point (2, �3) and... (answered by reviewermath)

Which equation represents the line that passes through the point (1,5) and has a slope of (answered by Fombitz)

A line passes through the point (-4,-1) and has a slope of... (answered by Fombitz)

What is the equation of the line that has a slope of -2 and passes through the point (-1, (answered by mananth)

A line passes through the origin and has a slope of 1/3. A point on the line is (t,... (answered by richwmiller)