# Find an equation of the line that is parallel to `y=3/4 x -1` and passes through the point (4,0). Find an equation of the line that is perpendicular to `y=x+4` and through the point (-7, 1).

baxthum8 | Certified Educator

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An equation paralle to `y= 3/4x-1` and passes through the point (4,0).  Since the equation is written in slope intercept form the line has a slope of `3/4` .

In order to be parallel the line must havet he same slope, `3/4.`

Use point slope form `y - y_(1)= m(x-x_(1))` , to write the equation of the line.

`y - 0 = 3/4(x-4) rArr y = 3/4x - 3`

A line perpendicular to `y = x+4` , must have a slope of `-1` as this is the opposite reciprocal of the line's slope of 1.

Again use point...

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mlehuzzah | Certified Educator

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ksri | Student

y = 3/4 x - 1

Any straight line parallel to the given line will be of the form

y = 3/4 x + k

When this line passes through the point ( 4 , 0 ) we have

0 = 3/4 * 4 + k

Hence k + 3 = 0 .

k = - 3 .

Hence y= 3/4 x - 3  is the required equation.

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y = x + 4

That is x - y + 4 =0  is the given line .

Any line perpendicular to this line will be of the form

x + y +k =0 .

Since this passes through the point ( - 7 , 1 )

1 - 7 + k = 0 .   ......  That is k = 6

Hence the required equation is x + y + 6 = 0 ..