I am looking for a perpendicular line. I'd appreciate ir if you could tell me if I'm on the right track. I am given y=-5x + 4 and know that a perpendicular line passes through (3,5). I think the slope of this line would be 1/5 so it would go up (rise) 1, so the y point would be 6 and it would go over 5 places so x would be 8. I have to come up with the perpendicular line using slope intercept notation. Am I even close? Thanks!!!

Question

I am looking for a perpendicular line. I'd appreciate ir if you could tell me if I'm on the right track. I am given y=-5x + 4 and know that a perpendicular line passes through (3,5). I think the slope of this line would be 1/5 so it would go up (rise) 1, so the y point would be 6 and it would go over 5 places so x would be 8. I have to come up with the perpendicular line using slope intercept notation. Am I even close? Thanks!!!

Answer 1

since you know the slope is 1/5 you know the new equation must be

y = (1/5)x + b, but you also know that (3,5) lies on it, so...
5 = (1/5)(3) + b , multiply by 5
25 = 3 + 5b
22 = 5b
b = 22/5

so the equation in the form asked for is

y = (1/5)x + 22/5

Answer 2

Great...thanks for the clear explanation!:)

Answer 3

Yes, you are on the right track! To find a perpendicular line to a given line, you need to remember that the slopes of perpendicular lines are negative reciprocals of each other.

The given line is y = -5x + 4. To find the slope of this line, you can compare it with the slope-intercept form (y = mx + b) of a line, where m represents the slope. In this case, the slope (m) of the given line is -5.

To find the slope of the perpendicular line, you take the negative reciprocal of -5. The negative reciprocal of a number is the negative of its reciprocal. The reciprocal of a number is obtained by flipping the fraction. So, the negative reciprocal of -5 is 1/5.

You correctly determined that the slope of the perpendicular line is 1/5.

To find the equation of the line using slope-intercept form (y = mx + b), you have the slope (1/5) and a point (3,5) that the line passes through. You can substitute these values into the equation and solve for the y-intercept (b).

Using the slope-intercept form, you have:
5 = (1/5)(3) + b

Simplifying:
5 = 3/5 + b

To isolate b, subtract 3/5 from both sides:
5 - 3/5 = b
(25/5) - (3/5) = b
22/5 = b

So, the y-intercept (b) of the perpendicular line is 22/5. Now you have the slope (1/5) and the y-intercept (22/5) for the perpendicular line.

Therefore, the equation of the perpendicular line in slope-intercept form is y = (1/5)x + 22/5.