write the slope intercept equation for the line passing through the point (-4,5) and perpendicular to the graph equation 7x-2y=1

Question

write the slope intercept equation for the line passing through the point (-4,5) and perpendicular to the graph equation 7x-2y=1

Answer 1

Hi Kayla.

 

The slope of a perpendicular line is the "flip and change sign" of the original slope.  Mathematically we call that the opposite reciprocal.    Or can say that the orignial slope multiplied by the perpendicular slope = -1.

 

Here is how it works in this problem:

 

Our equation is to be perpendicular to 7x-2y=1.  So if you rearrange this into slope-intercept form, you will be able to find the slope of the line we want to be perpendicular to.

 

Add 2y to both sides

 

7x = 2y + 1

 

Subtract 1 from both sides

 

7x-1 = 2y

 

Divide both sides by 2

 

(7/2) x - (1/2) = y

 

So the slope of the line we want to be perpendicular to is (7/2), so the slope we want to use is the flip (2/7) and change sign -(2/7) of this.

 

Now our challenge is to write and equation that passes through (-4, 5) and has a slope of -(2/7).

 

Using y=mx+b, substitute in everything you know:

 

y= 5, x = -4, slope = -(2/7)

 

5=-(2/7)(-4) + b

 

5 = 8/7 + b

 

Subtract (8/7) from both sides

 

5-(8/7) = b

 

35/7 - 8/7 = b

 

27/7 = b

 

So now you have everything you need to write the slop-intercept equation :

 

y = -(2/7)x + (27/7)