SOLUTION: Can help me please? Find an equation in standard form for the line described. - Through Q(-3,2) and parallel to the line containing (2,3) and (1,-2) THANKS FOR ALL YOUR HE

Algebra ->  Linear-equations -> SOLUTION: Can help me please? Find an equation in standard form for the line described. - Through Q(-3,2) and parallel to the line containing (2,3) and (1,-2) THANKS FOR ALL YOUR HE      Log On


   

Question 265599: Can help me please?
Find an equation in standard form for the line described.
- Through Q(-3,2) and parallel to the line containing (2,3) and (1,-2)
THANKS FOR ALL YOUR HELP!
Found 3 solutions by josmiceli, solver91311, checkley77:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The reasoning steps are:
(1) If 2 lines are parallel, they have the same slope
(2) If you know 2 points, you know the equation of the
line through those 2 points
First, I'll find the equation of the line through
P[1](2,3) and P[2](1,-2)
The general equation is:

----------------------------
given:
x%5B1%5D+=+2
y%5B1%5D+=+3
x%5B2%5D+=+1
y%5B2%5D+=+-2
%28y+-+3%29%2F%28x+-+2%29+=+%28-2+-+3%29%2F%281+-+2%29
%28y+-+3%29%2F%28x+-+2%29+=+-5%2F-1
%28y+-+3%29%2F%28x+-+2%29+=+5
y+-+3+=+5%2A%28x+-+2%29
y+-+3+=+5x+-+10
y+=+5x+-+7
This is in the general form y+=+mx+%2B+b
where m is the slope, so the slope
of this equation is 5, and any line that
is parallel to it has slope = 5
----------------------------------------------
Now I have to find the line through Q(-3,2)
with m+=+5
Since the general form for a line is y+=+mx+%2B+b,
I can plug in values for x,y,and m, and then find b
2+=+5%2A%28-3%29+%2B+b
2+=+-15+%2B+b
b+=+17
So the equation is
y+=+5x+%2B+17, and in standard form:
5x+-+y+=+-17

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Parallel lines have equal slopes. Use the slope formula to calculate the slope of the line that contains the points (2,3) and (1,-2).



where and are the coordinates of the two given points.

Once you have calculated the slope of the line containing the points (2,3) and (1,-2), use that slope and the coordinates of point Q in the point slope form of the equation of a line to write the desired equation.



Where is the slope you just calculated and are the coordinates of point Q.

John

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
Through Q(-3,2) and parallel to the line containing (2,3) and (1,-2)
Y=mX+b
m=slope
b=Y intercept
m=(-2-3)/(1-2)
m=-5/-1
m=5
3=2*5+b
3=10+b
b=3-10
b=-7 the Y intercept.
Y=5X-7 (red line)
A parallel line will also have a slope=5
2=5*-3+b
2=-15+b
b=2+15
b=17 the Y intercept.
Y=5X+17 (green line)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+20%2C+5x+-7%2C+5x+%2B17%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 20, of TWO functions 5x -7 and 5x +17).