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# Trigonometry Question Help!

Can you help me with my trigonometry 1 question assignment? Can you also provide an explanation to support the answer?

1. What us the slope of any line perpendicular to the line 4x-2y=10?

a. (-1)/(3)
b. -1
c. -2

4x-2y=10
-2y=-4x+10
y=2x-5 is the slope-intercept form of the line:in general, y=mx+b where m is the slope and b is the y-intercept
the slope of any line perpendicular to this line will be the negative reciprocal of this line's slope
another way of saying this is that two lines are perpendicular if and only if the product of their slopes is -1
the answer to your question is not listed in a), b), or c)
Generally Speaking equation of a line is given by

Y = mx + b   is a binomial ( contains 2 terms, one for X , and the other for constant)

m is the slope= difference in y coordinate of 2 points of the line/ difference in X coordinate of 2 points.

The distinct feature of a line is : that slope between every 2 points of a line is constant, and is that geometric property of line which leads to derive the equation as

Y = mx +b

Now another geometric property indicates that the relationship between slope of 2 perpendicular lines

(m1, m2 ) is such that:

m1 = - 1/ m2

To put this into algebraic form

Consider 2 lines given:

L1 :  m1 X + b1
L2 :  m2 X + b2

L1 is perpendicular to L2

if and only if   m1 = - 1/m2

Here You have your L1 given as  4X -2y =10

Put it in the form of  Y = m1x +b

and from there find out m2. By using the property explained in here.

Hi Paige,

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