Question

Write an equation in slope-intercept form perpendicular to the given equation through the given point

Y = -3x + 4
(6,-2)

Answer 1

The equation in slope-intercept form perpendicular to the given equation
`y = -3x + 4` through the given point (6,-2) is
`\mathbf{y=(1)/(3)x}`

Explanation:

We need to write an equation in slope-intercept form perpendicular to the given equation through the given point

y = -3x + 4

(6,-2)

The general equation in slope intercept form is:
`y=mx+b` where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding slope:

The given line is perpendicular to required line, so there slopes are opposite

The slope of given line
`y = -3x + 4` is m = -3, (By comparing it with general equation y=mx+b, we get m = -3)

The slope of required line is:
`m = (1)/(3)`

Finding y-intercept:

y-intercept can be found by using slope
`m = (1)/(3)` and the point(6,-2)

`y=mx+b\\-2=(1)/(3)(-6)+b\\-2=-2+b\\b=-2+2\\b=0`

So, we get y-intercept b =0

Equation of required line:

So, the equation of required line having slope
`m = (1)/(3)` and y-intercept b =0 is:

`y=mx+b\\y=(1)/(3)x+0\\y=(1)/(3)x`

So, the equation in slope-intercept form perpendicular to the given equation
`y = -3x + 4` through the given point (6,-2) is
`\mathbf{y=(1)/(3)x}`