## starrhunter 3 years ago What is the equation of the line that passes through the point (4, 1) and is perpendicular to the line y = –2x + 4?

1. Mertsj

Do you know point-slope form of the equation of a line?

2. starrhunter

no i dont know any algebra im trying to help my sister finish her assignments. shes in the hospital. i dont need anyone to teach me anything i just dont want her to fail. any good answers anyone has is greatly appreciated

3. Mertsj

Sorry. It is contrary to the code of conduct to just post answers. Too many kids try to avoid learning that way.

4. starrhunter

could u show me how to work it out then? dont want anyone to get in trouble.

5. Mertsj

\[y-y _{1}=m(x-x _{1})\]

6. AsianStudent_01

First, determine the slope of the given line. x + 2y = 6 Solve for y to get this in slope-intercept form. Remember to switch signs when you switch sides. 2y = -x + 6 Divide all terms on both sides by 2. y = -0.5 x + 3 So the slope of the given line is the coefficient of x, which is -0.5 = -1/2 The slope of a perpendicular line is the negative reciprocal of that slope, which would be 2. Use the point-slope form to build the equation with the point (4,2) y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. y - 2 = 2(x - 4) This is an equation that satisfies the question. To get this into slope-intercept form, expand, simplify and solve for y. y = 2x - 8 + 2 y = 2x - 6

7. Mertsj

That is point-slope form. The given line has slope -2 so the perpendicular has slope 1/2 replace y1with 1, m with 1/2 and x1 with 4 and simplify. That will be the equation of the desired line.

8. AsianStudent_01

Yep, take it with a little grain of salt

9. starrhunter

so what do i have to simplify exactly?

10. Keroro

|dw:1338928449474:dw|

11. Keroro

and make y the subject of the formula

12. Mertsj

To simplify, distribute the 1/2 and then add 1 to both sides.

13. starrhunter

y = 1/2x- 1??

14. Mertsj

Very good!!

15. Mertsj

I knew you could do it.