Question

What is an equation of a line that is perpendicular to the line whose equation is 2y+3x=1?

Answer 1

4x - 6y = 3

Step-by-step explanation:

To find the slope of the original line, we can put the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To do this, we can solve for y:

`2y+3x=1`

Subtract 3x on both sides

`2y=-3x+1`

Divide by 2

`y=-(3)/(2)x+(1)/(2)`

The slope of the original line is
`-(3)/(2)`. The negative reciprocal of this is
`(2)/(3)` (flip the fraction and change the sign) which becomes the slope of the perpendicular line.

To find the equation of the perpendicular line, we can use the point-slope form of the equation of a line, which is:
`y-y1=m(x-x1)` where x1 and x2 is a point on the line and m is the slope.

We can choose any point on the line; for simplicity, we can choose the y-intercept of the original line, which is (0, 1/2).

`y-(1)/(2) = (2)/(3)(x-0)\\`

Simplify

`y-(1)/(2) =(2)/(3) x`

Multiply by 6 to eliminate fractions

`6y-3=4x`

Rearrange terms

`4x-6y=3`