slope intercept equation

Question

Write a slope intercept equation for a line parallel to the line x-8y=3 which passes through the point (16,-5)

Answer 1

Just a different way of doing it...

 

 

 

Get this into y = mx + b format so you will know the slope, m.

x - 8y = 3

 

 

Subtract x from both sides.

-8y = -x + 3

 

Divide both sides by -8:

y = (1/8)x -3/8

 

So m = 1/8.

 

Since line is parallel to y=(1/8)x - 3/8, it's slope must also be 1/8.

 

 

Use point-slope formula with (16, -5).

 

y - y₁ = m (x - x₁)

 

y - (-5) = (1/8) (x - 16)

 

y + 5 = (1/8)x - 2

 

Subtract 5 from both sides:

y = (1/8)x - 2 - 5

 

y = (1/8)x - 7

 

 

Answer 2

x - 8y = 3

 

move variables around so it's in the form:     y = mx + b

 

what we need is just the slope which is m.

 

x - 3 = 8y

 

divide both sides by 8:

 

y = (1/8)x - 3/8

 

so m is 1/8.

 

any line parallel to the given line will also have a slope of 1/8.

 

so using this slope (1/8) and the given point(16, -5):

 

-5 = (1/8)16 + b

 

-5 = 2 + b

 

so,

 

b = -7

 

therefore,

 

y = (1/8)x - 7

 

Answer 3

Hi Kimikio;

x-8y=3, first equation

(16,-5), second equation coordinate

 

We will begin by placing the formula into the format of...

y=mx+b

m=slope

b=y-intercept, the value of y when x=0

 

x-8y=3

Let's isolate y...

Let's subtract x from both sides...

-x+x-8y=3-x

-8y=3-x

Let's divide both sides by -8...

(-8y)/-8=(3-x)/-8

y=(-3/8) + (x/8)

or

y=(x/8)-(3/8)

 

The slope is 1/8.  The line parallel to this must have the same slope, but different y-intercept.

So...

y=(x/8) + b

If you will notice, I changed the - sign to a + sign.  This is because I do not yet know if the y-intercept is positive or negative.  Adding a negative number is the same thing as subtracting a positive number.

 

Let's plug-in our coordinates..

(16,-5)

y=(x/8) + b

-5=(16/8) + b

-5=2+b

-7=b

y=(x/8) - 7