Find the equation of the line parallel to y-axis and drawn through the point of intersection of lines x-7y+5=0 and 3x+y=0?
To find the equation of the line parallel to the y-axis and passing through the point of intersection of two lines, we first need to find the intersection point of the given lines.
Given lines:
1) x - 7y + 5 = 0
2) 3x + y = 0
To find the intersection point, we can solve these two equations simultaneously.
Step 1: Solve equation 2 for y:
y = -3x
Step 2: Substitute y from Step 1 into equation 1:
x - 7(-3x) + 5 = 0
x + 21x + 5 = 0
22x + 5 = 0
22x = -5
x = -5/22
Step 3: Substitute x into equation 2 to find y:
3(-5/22) + y = 0
-15/22 + y = 0
y = 15/22
Therefore, the intersection point is (-5/22, 15/22).
Now, since we need to find a line parallel to the y-axis passing through this point, we know that x will always be the same value (-5/22) for any y-coordinate.
Thus, the equation of the line is x = -5/22.
Therefore, the equation of the line parallel to the y-axis passing through the point of intersection is x = -5/22.
Since the equation of a line parallel to the y-axis has the form x = k, where k is a constant, all we need is the x-value of the point of intersection of your 2 lines.
From the 2nd, y = -3x
sub that into the first:
x - 7(-3x) + 5 = 0
22x = -5
x = -5/22 , that's it! All done.