# Find the equation of the line passing through the point (5,7) and parallel to the line 5x+4=0.

lemjay | High School Teacher | (Level 2) Senior Educator

Posted on

Simplify the given equation. To do so, subtract both sides by 4

`5x + 4 = 0`

`5x+ 4 - 4 = 0 -4`

5x = -4

Then, divide both sides by 5.

`(5x)/5 = -4/5`

`x = -4/5`

Since it has only one variable which is x, the graph of the given equation is a vertical line.

This means that  the line parallel to 5x+ 4 = 0 will also be vertical.  And a vertical line has no slope.

So the equation of the line that is parallel to 5x +4 = 0 and passes to (5, 7) will be equal to the x-coordinate of the point.

`x = 5`

By subtracting both sides by 5, we may re-write it as:

`x - 5 = 5-5`

`x - 5 = 0`

Hence, the equation of the other line is `x - 5 = 0` or simply `x = 5` .

vaaruni | High School Teacher | (Level 1) Salutatorian

Posted on

given that require line is parallel to the line 5x-4=0

since equation of the line 5x-4 = 0 has only one variable x and does not

have 'y' which shows that value of y=0 i.e. the line is parallel to y-axis.

and any line parallel to this line 5x-4=0  also will have y=0.

Now since the require line passes through the point (5,7) therefore

equation of the require line =>   x-5 =0  <-- Answer