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## slope intercept equation

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

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

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

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