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Question 92217: I need help with this problem. I'm not understanding what it is I should do.
Write the equation of the line passing through (-2,17) and (-1,12)
Please help I'm getting really frustrated.
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write the equation of the line passing through (-2,17) and (-1,12)
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slope = [12-17]/[-1--2] = -5/1 = -5
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The equation you want is y=mx+b where m=-5 and y=12 when x=-1
Substitute these values and solve for "b".
12 = -5*-1+b
12 = 5+b
b = 7
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EQUATION:
y = -5x+7
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Cheers,
Stan H.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Write the equation of the line passing through (-2,17) and (-1,12)
.
Let's just think our way through this problem.
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One of the things that would really help us is if we knew the slope of the graph. We are
given two points on the graph. Suppose we draw a line connecting those two points. Then
we need to find the slope of that line.
.
We know that slope is defined as the change in y divided by the change in x as you move from one
point to the other.
.
Looking at the two points, let's try to picture moving along the graph from the point (-2, 17)
to the point (-1,12). The change in x is +1 because we go from a -2 right to -1. That
is a move in the positive direction (to the right is positive). So we have found that the
change in x is +1.
.
Now let's find the change in y. Again we have to move from the first point where y is 17
to the second point where y is 12. That is a change of -5 because we are moving downward and
down is in the direction of negative y. So our change in y is -5.
.
So the slope ... being the change in y divided by the change in x ... is -5 divided by
+1 which is -5.
.
Good ...
.
Now we can go to the slope-intercept form of an equation. This form says that in the equation:
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y = mx + b
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m is the slope and b is the value where the graph crosses the y axis.
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We already know the slope is -5 so we can substitute -5 for m in the equation to get:
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y = -5x + b
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Next we need to find the value for b ... the point where the graph crosses the y-axis.
We can do this by using one of the two points we were given. Suppose we use the point
(-2, 17). Since this point is on the graph, we know that when x = -2 and y = 17, the equation
must be satisfied. So let's go to the equation y = -5x + b and substitute those two values
for x and y. When we do our equation is:
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17 = -5(-2) + b
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Multiplying out on the right side we get:
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17 = 10 + b
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Get rid of the 10 on the right side by subtracting 10 from both sides of the equation to
get:
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7 = b
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Now we know b and we can substitute that into our equation to get:
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y = -5x + 7
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There it is ... an equation that will work. Let's check it using the second point. From
the second point we were given we know that when x = -1 and y = 12 the equation has to work
because that is a point on the graph. Let's substitute -1 for x and +12 for y in our
equation and see if it balances. Substitution results in:
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12 = (-5)(-1) + 7
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Multiply out the right side to get:
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12 = +5 + 7
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And you can see that the right side equals the left side ... so our equation works.
.
We are done ... and equation that will work is y = -5x + 7
.
Hope this helps you to understand the problem a little better.
.
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