How do you write an equation of the line that passes through 3,4 and is parallel to y = -2?

Asked on by qtpie2013

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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).




krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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

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