Question 19578: Please help me find the equation of the line through (-3,7) that is paralled to the line joining the points (4,5) and (-2, -8). Thank you in advance.
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
To write the equation of a parallel line, we first need to know the slope that it is parallel to.
Use the slope formula to find the slope of the line passing through the points (4, 5) and (-2, -8).
In case you have not memorized this important formula, it is the difference of the y-coordinates divided by the difference between the x-coordinates.
In other words, if the points are (a, b) and (c, d), then the slope is:
m = (d - b)/(c - a)
Using this formula with the two points gives us:
m = (-8 - 5)/(-2 - 4)
m = -13/(-6)
m = 13/6
Now that we have the slope for our line, we use the point-slope formula to write the equation of the line with slope 13/6 passing through the point (-3, 7).
Given a slope of m and the point (a, b), the point-slope formula is:
y - b = m*(x - a)
(The asterisk means multiplication.)
So, we have:
y - 7 = (13/6)*(x + 3)
Get rid of the parantheses by multiplying both the x and the 3 by 13/6 (this is the distributive property).
y - 7 = (13/6)*x + 13/2
Add 7 to both sides to solve for y.
y = (13/6)*x + 27/2
This is the slope-intercept form of the equation. We can also write it in general form. Multiply both sides by 6 to clear the fractions.
6*y = 13*x + 81
Subtract 6*y from both sides to set the equation equal to zero.
13*x - 6*y + 81 = 0
~ Mark
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