SOLUTION: Write an equation of the line containing the given point and perpindicular to the give line. (3, -7); 3x+ 2y =5 Also write an equation of the line containing the given point and

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line containing the given point and perpindicular to the give line. (3, -7); 3x+ 2y =5 Also write an equation of the line containing the given point and       Log On


   

Question 457117: Write an equation of the line containing the given point and perpindicular to the give line. (3, -7); 3x+ 2y =5
Also write an equation of the line containing the given point and parallel to the given line. (-4,3); 6x = 5y+8.
I dont just want the answers I honestly want to understand how to do this, please help!!

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation of the line containing the given point and perpendicular to the give line. (3, -7); 3x + 2y = 5
:
Find the slope of the given equation, put it in the slope/intercept form: (y = mx+b)
3x + 2y = 5
Subtract 3x from both sides
2y = -3x + 5
divide both by 2
y = -3%2F2x + 5%2F2
m1 = -3%2F2
The slope relationship of perpendicular lines: mi*m2 = -1
-3%2F2*m2 = -1
m2 = -1 * -2%2F3
m2 = 2%2F3 is the slope of the perpendicular line
Find the equation of the perpendicular line using the point/slope form (y-y1=m(x-x1)
x1=3, y1=-7, m = 2%2F3
:
y - (-7) = 2%2F3(x - 3)
y + 7 = 2%2F3x - 3*2%2F3
y = 2%2F3x - 2 - 7
y = 2%2F3x - 9, the equation perpendicular to 3x + 2y = 5
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Also write an equation of the line containing the given point and parallel to the given line. (-4,3); 6x = 5y+8.
Find the slope the of the given equation
6x = 5y + 8
5y = 6x - 8
Divide both sides by 5
y = 6%2F5x - 8%2F5
parallel lines have the same slope, therefore:
y - 3 = 6%2F5(x - (-4))
y - 3 = 6%2F5(x + 4)
see if you can finish this the same way we did the first problem