Write the equation of a line in slope-intercept form that has a slope of -1/4 and passes through the point (8, -1). Slope should be a reduced improper fraction.

Question

mathstudent55 · Answer

The slope-intercept form of the equation of a line is:
$y = mx + b$
where 
$m$ = slope, and
$b$ = the y-intercept

mathstudent55 · Answer

You are told that the slope is $ -\dfrac{1}{4} $, so you can already substitute that value into m in the equation:

$ y = -\dfrac{1}{4}x + b $

anonymous · Answer

okay so I would set it up something like this |dw:1374387185609:dw|

mathstudent55 · Answer

Now you need to find $b$.

To do that, use the point you are given, (8, -1), and replace $x$ with 8 
and $y$  with -1 in the equation. Then solve for $b$:

$y = -\dfrac{1}{4}x + b$

$-1 = -\dfrac{1}{4}(8) + b$

$-1 = -2 + b$

$1 = b$

Now that we know $b = 1$, just substitute 1 for b in our equation:

$y = -\dfrac{1}{4}x + 1$

anonymous · Answer

but the 1 is a negative isnt it?

mathstudent55 · Answer

No, it's positive.

anonymous · Answer

oh.

mathstudent55 · Answer

Look at our result:

$y = -\dfrac{1}{4}x + 1 $

Just from looking at it, you can see the slope is $ -\dfrac{1}{4} $.

Now let's test point (8, -1):

$y = -\dfrac{1}{4}x + 1 $

$-1 = -\dfrac{1}{4}(8) + 1 $

$-1 = -2 + 1 $

$-1 = -1 $

Since -1 = -1 is a true statement, that means (8, -1) is a point on the line.

The line has the slope we need, and the point we were asked about is on the line, so the equation of the line is correct with b = 1.

anonymous · Answer

so that's the answer. b=1...?

mathstudent55 · Answer

The answer is the equation:

$y = -\dfrac{1}{4}x + 1 $

anonymous · Answer

But how would I put that into an improper fraction?

mathstudent55 · Answer

The slope here happens to be $-\dfrac{1}{4} $.
It is reduced, but since it's not an improper fraction, it can't be written as one.

Did you by any chance miscopy the problem? Did your problem by any chance ask to find the line that is perpendicular to a line with slope $-\dfrac{1}{4} $?

anonymous · Answer

uhm.. No, it didn't. So i guess it cant be reduced or made into an improper fraction, that would be the answer?

anonymous · Answer

oh, never mind I got the answer  :3 thanks for the help

mathstudent55 · Answer

It is reduced. It simply is not an improper fraction.

mathstudent55 · Answer

You're welcome.