Question

Find an equation for the line perpendicular to the line – 2x + 4y = 2 having the same y-intercept as – 7x + 6y = -3.

Answer 1

Let's find the y-intercept of the line with equation

`-7x+6y=-3`

To get the y-intercept, we plug in "0" into "x". So,

`\begin{gathered} -7x+6y=-3 \\ -7(0)+6y=-3 \\ 6y=-3 \\ y=(-3)/(6) \\ y=-(1)/(2) \end{gathered}`

So, the coordinate point is

`(0,-(1)/(2))`

We need to find the equation of the line that is perpendicular to the line with equation -2x + 4y = 2 and passes through the point (0, -1/2).

First, let's re-arrange -2x + 4y = 2 into the form y = mx + b, where m is the slope and b is the y-intercept.

`\begin{gathered} -2x+4y=2 \\ 4y=2x+2 \\ y=(2x)/(4)+(2)/(4) \\ y=(1)/(2)x+(1)/(2) \end{gathered}`

We know the line perpendicular will have a slope that is negative reciprocal.

So, the perpendicular line will have a slope of

`-2`

So, the line will take the form:

`y=-2x+b`

Since it goes through the point (0, -1/2), we can solve for "b":

`\begin{gathered} y=-2x+b \\ -(1)/(2)=-2(0)+b \\ -(1)/(2)=b \\ \end{gathered}`

Thus, the equation of the linne is,

`y=-2x-(1)/(2)`