## kcbrosell 3 years ago find an equation for the line with the given properties Question: Perpendicular to the line x − 2y = −5; containing the point (0, 4)

1. myininaya

so put that equation in this form: y=mx+b

2. myininaya

so we can find the slope of the perpendicular line after we do that

3. myininaya

Do you need help putting in that form?

4. MrYantho

1. Convert equation to y=mx+b, to find slope 2. Our second slope is the negative reciprocal of the given line's slope 3. Substitute the new slope, and the values of x and y into y=mx+b to solve for b (the y-int)

5. kcbrosell

I am not understanding

6. myininaya

Do you know how to write the equation given in this form: y=mx+b?

7. kcbrosell

no i do not

8. myininaya

You are just trying to solve for y: $x-2y=-5$ $\text{ add } 2y \text{ on both sides }$ $x-2y+2y=-5+2y$ $x=-5+2y$ Now add 5 on both sides $x+5=2y$ Now divide both sides by 2 $\frac{x+5}{2}=y =>y=\frac{x}{2}+\frac{5}{2} =>\frac{1}{2}x+\frac{5}{2}$ so what is the slope here?

9. kcbrosell

1/5=5 & 2/2=1, is that right

10. myininaya

y=mx+b where is m is slope so what is in front of x up there? 1/2 right? so what is the slope of a perpendicular line to this one? in other words what satisfies this equation 1/2 * ? = -1

11. kcbrosell

-1/2

12. myininaya

close -2 would be the slope of the perpendicular line

13. myininaya

so we have all lines are in this form y=mx+b => this line has this form: y=-2x+b

14. myininaya

now we know a point on the line (0,4)

15. myininaya

where x=0 and y=4 so we have enough info to find b replace x with 0 and y with 4 4=-2(0)+b how do you solve this for b?

16. kcbrosell

wouldnt you multiply each side by -4

17. myininaya

4=0+b since -2(0)=0 4=b since 0+b=b

18. myininaya

so the equation us y=-2x+4