Math QUESTION 3

Question

Find an equation for the line perpendicular to y=−17x+6 and goes through the point (−8,3) answer in the form y=mx+b.

Answer 1

Hi Bon, so they are giving you an equation in slope-intercept form and asking you to find the line that is perpendicular but goes through the given point

Here's a little how to guide:

1. Find perpendicular slope by taking the negative reciprocal of the given slope (take the opposite sign and flip the fraction). 
2. the given slope is -17/1 so the negative reciprocal would be +1/17
3. Use the perpendicular slope you found and the given point to plug into y=mx+b and solve for b so you can get your new equation. given point: (-8,3)

y = mx + b

3 = 1/17(-8) + b

3 = -8/17 + b

+8/17 +8/17

3 8/17 = b

3. Now use the perpendicular slope for "m" and the value for "b" you found to form your new equation:

y = 1/17x + 3 8/17

**There is another way to complete this using point slope form: y - y₁ = m(x - x₁)

After you've found the negative reciprocal slope, use point slope form to plug in for your new slope "m", the given point x-value for x₁ and the y-value for y₁ and then move terms into the y=mx+b form using your equation skills:

y - 3 = 1/17(x-(-8)) *add the opposite in the ()

y - 3 = 1/17(x + 8) *now distribute -1/17 across ()

y - 3 = 1/17x + 8/17 *remember you want it in the form y=mx+b so move the 3

+3 +3

y = 1/17x + 3 8/17

Either way you get the same answer and that's also a great built-in check step strategy during tests and quizzes!

Answer 2

The equation (and line) perpendicular have slopes that are negative reciprocals of the origin line. In this case that is 1 / 17.

Use point-slope form

(y - 3) = (1/17)(x + 8)