find the slope and y-intercept for 4x-2y=8

Question

Having trouble finding the slope perpendicular to the problem above as well, Please help and thank you so much 

Answer 1

Hello, Jasmine

Let me try to explain to you how you find the slope of a line that is perpendicular to a given line. In order for a line to be perpendicular to a given line, its slope must be NEGATIVE RECIPROCAL to the slope of the given line.  Let me break it down for you.

 

a) NEGATIVE: it does not mean that the number is going to be negative, but it means that it will be its opposite.  For example, the opposite of -8 is 8, the opposite of -(3/4) is 3/4, the opposite of 2 is negative 2.  

b) RECIPROCAL: You were probably first introduced to the concept of reciprocal when you were dividing fractions.  Remember "flipping the fraction upside down"? That's a reciprocal.  For instance, the reciprocal of 8 is 1/8, the reciprocal 5/8 is 8/5.

 

Now that you know what the words mean, let's find the negative reciprocal of some numbers.

a) 5, its negative reciprocal is -(1/5).

b) 2/3, its negative reciprocal is -(3/2)

c) -(4/5), its negative reciprocal is 5/4

 

So, Jasmine as John mentioned, to find the slope of a line rewrite it in the slope intercept form.  Let say you have 5x-2y= 8, which is the standard form. To find the slope,

 

5x-2y.        = 8                     Subtract 5x from both sides

-5x              -5x

    -2y        = -5x+ 8             Divide by -2

      y          = -(5/2)x-4

Then, the slope will be -5/2 and the y-intercept will be -4.  A line perpendicular to this line will have a slope of 2/5, since 2/5 is the negative reciprocal of -5/2.

 

I hope this helps a little. Thanks for posting your question.

 

D.Y. Taylor

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Answer 2

One way to do this is to first rewrite the equation in Slope-Intercept form (y = mx + b, where m represents the slope of the line and b the y-value of the point of intersection of the line and y-axis):

 

4x − 2y = 8, 2y = 4x − 8 and y = 2x − 4.

 

In this form, we can see that the slope of the line is 2 and the y-intercept is −4 (which means the point (0,−4)). The slope of any line that is perpendicular to this one is the negative reciprocal of the slope of this line or −1/2.