SOLUTION: Use the given conditions to write an equation for each line in point-slope form. Passing through (2, -3) and perpendicular to the line whose equation is y = 1/5 x + 6.

Question 977443: Use the given conditions to write an equation for each line in point-slope form.
Passing through (2, -3) and perpendicular to the line whose equation is y = 1/5 x + 6.
Found 3 solutions by Cromlix, Fombitz, anand429:
Answer by Cromlix(4381)   (Show Source): You can put this solution on YOUR website!
Hi there,
A line that is perpendicular to another
line have the product of their gradients
equaling -1 {(m(1) x m(2) = -1}
With y = 1/5x + 6. The gradient is 1/5
so, 1/5 x m(2) = -1
m(2) = -5
The line that passes through (2,-3)
has the equation:-
y - (-3) = -5(x - 2)
y + 3 = -5x + 10
y = -5x +10 - 3
y = -5x + 7
Hope this helps:-)
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Perpendicular lines have slopes that are negative reciprocals.

So then,

.
.
.
.

Answer by anand429(138)   (Show Source): You can put this solution on YOUR website!
Let required line be of form y = mx+c (slope-intercept form)
Since it is perpendicular to y = 1/5 x + 6
So, product of slopes = -1 (for two perpendicular lines m1 * m2 = -1)
So m * (1/5) = -1
=> m=-5
So our line becomes,
y = -5x + c
Now, this line passes through (2,-3) (As per ques.)
So putting the coordinates in above equation,
-3 = -5*2 +c
=> c = 7
So our line becomes,
y = -5x + 7.
Alternate method (Point slope form)
Using standard point-slope form and the condition that our line passes through (2,-3),we can write,

Now , we have already found m as in previous solution as m=-5
So, our line is:

=> (Ans. in point slope form)
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