OpenStudy (anonymous):

Write an equation in slope-intercept form for the line that is perpendicular to the given line and that passes through the given point. 1) 2x+3y=7; (4,5) 2) -2x - 8y= 16; (4,5) 3) y = x -5; (0,5)

2 years ago
OpenStudy (danjs):

perpendicular line will have a slope that is the negative reciprical of the given line

2 years ago
OpenStudy (danjs):

for example #3 y = x - 5 Slope = 1 Perpendicular slope -1

2 years ago
OpenStudy (danjs):

Use point-slope formula to make a line equation from a point (x1,y1) and a slope (m) y - y1 = m*(x-x1)

2 years ago
OpenStudy (danjs):

To begin #1, write 2x + 3y = 7 in y = m*x + b form

2 years ago
OpenStudy (anonymous):

So what does the b stand for? and how do we know what to put there?

2 years ago
OpenStudy (danjs):

Slope-Intercept form of a line y = m*x + b m = slope b = y-intercept

2 years ago
OpenStudy (anonymous):

Okay that makes sense..

2 years ago
OpenStudy (danjs):

1) 2x + 3y = 7 Rearrange to the form , y = m*x+b 3y = -2x + 7 y = (-2/3)*x + (7/3) Slope m = -2/3 --------------------------------- A line perpendicular to that line will have a slope that is the negative reciprical of -2/3 Slope of perpendicular line = +3/2

2 years ago
OpenStudy (danjs):

The equation for the perpendicular line will be: slope m = 3/2 point (x1,y1) = (4,5) y - y1 = m*(x-x1) Plug in the values y - 5 = (3/2)*(x - 4)

2 years ago
OpenStudy (danjs):

You can clean that up a little if you want, distribute the 3/2 into the x-4 and add 5 to both sides... y - 5 = (3/2)x - 4*(3/2) y = (3/2)x - 6 + 5 y = (3/2)*x - 1

2 years ago
OpenStudy (danjs):

same process for the next 2 probs.

2 years ago
OpenStudy (anonymous):

Okay, thank you so much for your help! Your a life saver!

2 years ago
OpenStudy (danjs):

You're welcome. Does it make sense now?

2 years ago
OpenStudy (anonymous):

Yes, you make way more sense then my math teacher does!

2 years ago
OpenStudy (danjs):

haha, if you want to try and work through #2, i can check if it is right, for practice if you want

2 years ago
OpenStudy (anonymous):

Okay, would #2 be y= 2/8*x-1?

2 years ago
OpenStudy (danjs):

2) -2x - 8y= 16; (4,5) rearranging: y = (-1/4)x - 2 Slope = -1/4 ------------------------------ Perpendicular Line: slope m = 4 point (x1,y1) = (4,5) y - y1= m(x - x1) y - 5 = 4*(x - 4) y - 5 = 4x - 16 y = 4x - 11 ------------------------------- The Line; y = 4x - 11, is perpendicular to the line -2x-8y=16, and goes through the point (x,y) = (4,5)

2 years ago
OpenStudy (danjs):

Graph

2 years ago