SOLUTION: Hi, can i please get some steps on how to do this question: Find the value of "k" if the line y=-5/2x +2 is perpendicular to this line 4x+ky=7

Question 565299: Hi, can i please get some steps on how to do this question: Find the value of "k" if the line y=-5/2x +2 is perpendicular to this line 4x+ky=7
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your first equation is already in slope intercept form.
slope intercept form is y = mx + b
m is the slope and b is the y intercept.
the y intercept is the value of y when x = 0.
your second equation is in standard form.
standard form is ax + by = c
you need to convert the equation from standard form to slope intercept form before you do anything else.
start with 4x + ky = 7
subtract 4x from both sides of this equation to get:
ky = -4x + 7
divide both sides of the equation by k to get:
y = (-4/k)x + (7/k)
your 2 equations are now:
y = (-5/2)x + 2
y = (-4/k)x + (7/k)
if the lines are perpendicular, then their sloped are negative reciprocals of each other,.
the slope of the first equation is equal to (-5/2).
the negative reciprocal of (-5/2) is equal to (2/5)
since the line determined by your second equation is perpendicular to the line determined by your first equation, this means that:
(-4/k) = (2/5)
you can solve for k by doing the following:
equation is:
-4/k = 2/5
multiply both sides of this equation by k to get:
-4 = 2k/5
multiply both sides of this equation by 5/2 to get:
-4*5/2 = k
this makes k equal to -10
the slope of your second equation becomes:
slope = -4/k = -4/-10 = 4/10 = 2/5
2/5 is the negative reciprocal of -5/2 so we got the slope right.
your second equation becomes:
y = (2/5)x + 7/k
since k is equal to -10, your equation becomes:
y = (2/5)x - (7/10)
you can now graph these equations to see how they look.
the equations are:
y = -(5/2)x + 2
y = (2/5)x - (7/10)

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