Question

Find the equation of the line that is perpendicular to the given line and passes through the given point.

y = −1/2x − 3; (14, 0)

The equation is y = ?

Answer 1

`y=2x-28`

Explanation:

Slope intercept form:

`y=mx+b`

where:

• m is the slope (change in the y values over the change in the x values)
• b is the y-intercept (where x is 0)
• x and y are corresponding coordinate points (x,y)

When two lines are perpendicular, their slopes will be opposite reciprocals.

examples:

`(1)/(3)` → flip the fraction and change the sign →
`-3`

-5 or
`-(5)/(1)`→ flip the fraction and change the sign →
`(1)/(5)`

`(5)/(7)` →flip the fraction and change the sign →
`-(7)/(5)`

So find the opposite reciprocal of the given slope:

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

Flip the fraction and change the sign:

`-(1)/(2)` →
`(2)/(1)` or
`2`

Now insert the new slope and the given points into point-slope form:

`y-y_(1)=m(x-x_(1))\\\\(14_{x_(1)},0_{y_(1)})\\\\y-0=2(x-14)`

Solve the equation for y. Use the distributive property:

`y-0=2(x)+2(-14)\\\\y-0=2x-28`

Simplify:

`y=2x-28`

:Done