Two parallel lines have equal slopes. To find the slopes of the 2 lines, we have to put the equation of the lines in the standard form, which is:
y = mx + n, where m represents the slope and n is the y intercept.
We know, from enunciation, that the equation of one of the 2 lines is y = -2. From this equation, we conclude that the y intercept is -2, meaning that n = -2 and the slope is m = 0.
According to the rule, the slopes of 2 parallel lines are equal, we conclude that the slope of the other line is also m = 0.
We know that the line is passes through the point (3,4).
That means that the coordinates of the point verifies the equation of the line: y = mx+n.
4 = 0*3 + n (we've put the slope m = 0)
n = 4
So, the equation of the line, which is parallel to the line y = -2 and it passes through the point (3,4) is:
y = 4
To find the line passes through the coordinates (3,4) and is parallel to y = -2.
Any line that is parallel to y = -2 is of the form y = k, where k is any constant.
We decide the value of k by the fact that this line passes through the point (3,4).
So the point (3,4) should satisfy the equation y = k. Or
0x+y = K......(1)
Put (x,y) = (3,4) in the equation flagged at (1):
0*(3)+4 = k. This gives k = 4.
So the assumed equation y = k becomes , 0x+y = 4 or
y = 4 .
Therefore y= 4 is the straight which is parallel to y = -2 and passes thruogh the point (3,4).
A general equation of line is:
y = m x + c
In this equation m = slope of the line.
We can rewrite the given equation in this general form as:
y = 0*x - 2
This means that for this line value of m = slope of line = 0.
Any line parallel to this line will also have same slope of 0.
Therefore equation of such line will be:
y = c
To find equation of line passing through point (3, 4), substituting the value of y coordinate in the above equation:
4 = c
Therefore the equation of line becomes:
y = 4