|
Question 373624: Can some please help me !!
(-2,9);3x=7y+6
The equation of the line is y=
Write equation of the line containing the given point and parallel to the given line. Express your answer in the form y= m x+b
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
Write equation of the line containing the given point and parallel to the given line
Using the standard point-slope form for an equation of a line y = mx + b
where m is the slope and b the y-intercept.
3x = 7y+6 Solving for y to put the equation into the slope-intercept form
3x - 6 = 7y
(3/7)x - (6/7) = y Slope of this line is (3/7)
parallel lines have equal slopes
New line would be
y = (6/7)x + b Using ordered pair Pt(-2,9) to solve for b
9 + (12/7) = b
63/7 + (12/7) = b
75/7 = b
y = (6/7)x + 75/7
Answer by Edwin McCravy(20086)  (Show Source):
You can put this solution on YOUR website! Can some please help me !!
(-2,9);3x=7y+6
The other tutor made a mistake and used b for m.
Let's draw the given line by getting some points:
x | y
-5 | -3
2 | 0
9 | 3
and then draw a line through them like this one in green:
Now let's plot the point (-2,9) that we want to get the equation of a line
which when graphed will pass through:
First get the given equation
3x = 7y + 6
into the form y = mx + b
3x = 7y + 6
Write the left side on the right and the right side on the left,
because we want the y to end up on the left side.
7y + 6 = 3x
Add -6 to both sides:
7y + 6 = 3x
- 6 - 6
---------------
7y = 3x - 6
Now divide every coefficient and the number 6 by 7
 y =  x - 
y = x -
That is now in the form y = mx + b
and we can look at the coefficient of x and see that
the slope m is
All parallel lines have the same slope, so if we want to
get a line parallel to that one we will use the same slope
So the line we want the equation of will have the same
slope but it will have a different value for b.
So we write
y = x + b
Now we will substitute the x-value of the point (-2,9) which
is -2 for x, and we will substitute the y-value of the point
(-2,9), which is 9, for y in that equation:
9 = (-2) + b
Now we will multiply through by 7 to get rid of the fraction:
7*9 = 7*(-2) + 7*b
63 = 3(-2) + 7b
63 = -6 + 7b
Add +6 to both sides
63 = -6 + 7b
+6 +6
------------
69 = 7b
Now we will divide both sides by 7
 = 
= b
Finally we will substitute for b in y = x + b
and the desired equation is
y = x +
Now let's check by getting a couple points on the desired line
Let's draw the final line by getting some points:
x | y
5 | 12
12 | 15
-2 | 9
Now let's draw a line through those points and see if it looks
like the line (in red) is parallel to the green one:
The red line looks parallel to the green line, so we are right.
Edwin
|
|
|
| |
