Question

Question Write an equation of the line passing through the point A(−1, 5) that is perpendicular to the line y = 17x+4 . y = '

Answer 1

Answer:
`y = -(1)/(17)x + (84)/(17)`

Explanation:

Find a slope perpendicular to the equation
`y = 17x + 4` using the formula for finding a perpendicular slope (m₁ * m₂ = -1)

`17 * m = -1`

`m = -(1)/(17)`

Now that we have our slope, we can plug it into the slope-intercept formula to create our equation (we aren't done yet though).

`y = mx + b`

`y = -(1)/(17) + b`

We must find the y-intercept (the b variable) to complete our equation. We can do this by using the provided point (-1, 5) to do this. Simply take the x-coordinate -1 and y-coordinate 5 to substitute the values into the equation we made.

`y = -(1)/(17)x + b`

`(5) = -(1)/(17)(-1) + b`

`5 = -(1)/(17)*-1 + b`

`5 = (1)/(17) + b`

`b = (84)/(17)`

With the new y-intercept (b variable), we simply substitute this value back into our equation and we're done!

`y = -(1)/(17)x + b\\y = -(1)/(17)x + ((84)/(17))\\\\y = -(1)/(17)x + (84)/(17)`