SOLUTION: Find an equation of the line satisfying the given conditions.
Through (-4,3); perpendicular to -8x+5y=77
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Question 201322: Find an equation of the line satisfying the given conditions.
Through (-4,3); perpendicular to -8x+5y=77
Found 2 solutions by Earlsdon, RAY100:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Recall that if two lines are perpendicular, then their slopes are the negative reciprocal of each other, that is:
Let's find the slope of the given line:
Solve this equation for y so that you have it in the slope-intercept form: . Add 8x to both sides.
Now divide both sides by 5.
Compare this with:
and you can see that the slope .
The negative reciprocal of m is:
so, for the new equation, you can start by writing:
To find the value of b, you need to substitute the values of the x- and y-coordinates of the given point (-4, 3) and solve for b.
Simplify.
Subtract from both sides. Replace()
or...
Now you can write the final equation.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
For this problem, lets first find the slope of the original equation, using y=mx +b form, and then define the slope of the second eqn as, m2=-1/m1,perpendicular. Finally, we can define the eqn of the second line from the slope and the given point.
.
-8x +5y =77
5y = 8x +77
y = (8/5)x + 77/5
.
or from form ,,,,y= m x +b,,,m = (8/5)
.
m2= - 1/m1 = (-5/8)
.
Second eqn is , y= mx +b,,,,y = (-5/8) x +b
.
As it contains the point ( -4,3),,,,substitute
.
(3) = (-5/8) (-4) + b
.
3 = 20/8 +b
.
24/8 - 20/8 = 4/8 =1/2 = b
.
subst m,,and b,,in form eqn,, y = (-5/8)x + (1/2)
.
mult thru by 8
.
8y = -5x + 4
.
checking, subst ( -4,3),,,,8*3=(-5)(-4) +4 = 24 ,,,,ok
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