Complete the equation of the line through (-6,-5) (-4,-4)

 Jul 28, 2017

To figure out the equation of a line that passes through the given points (-6, -5) and (-4, -4), you must first know the standard form of a line. It is the following:



Let m = slope of the line

Let b = the y-intercept (the point where the line touches the y-axis)


The first step is to figure out the slope of the line. How do we do that, you may ask? All you do is remember the slope formula.




We already have enough information to calculate the slope, m. We do this by substituting the given points into the formula.


\(m=\frac{-5-(-4)}{-6-(-4)}\)Simplify the fraction into simplest terms by evaluating the numerator and denominator separately.
\(m=\frac{-5+4}{-6+4}\)Of course, subtracting a negative is the same as adding a positive. 
\(m=\frac{-1}{-2}\)The negatives in the numerator and denominator cancel each other out.


Great! We know the slope! Now, the only variable to figure out next is b, the y-intercept. We can do this by plugging in points of points on the line in the equation. 




In other words, to solve for b, you must plug in a point we know is one the line (either (-6,-5) or (-4,-4)) for x and y. I'll choose (-4,-4):


\(y=\frac{1}{2}x+b\)Plug in the coordinate (-4,-4) in its appropriate spots and then solve for b.
\(-4=\frac{1}{2}*-4+b\)Now, solve for b.
\(-4=-2+b\)Add 2 on both sides.


Now that we have solved for both m and b, the equation that passes through the points (-6,-5) and (-4,-4) is \(y=\frac{1}{2}x-2\).


Do you need your answer in point-slope form? No problem! Remember the point-slope form




Of course, m is the slope again. We have already calculated that. Let's substitute that in.




\(y_1\hspace{1mm}\text{and}\hspace{1mm}x_1\) represent a point on the line. You can either substitute the first or the second set of coordinates. It doesn't matter. However, in the end, your answer should be one of these:



 Jul 28, 2017
edited by TheXSquaredFactor  Jul 28, 2017
edited by TheXSquaredFactor  Jul 28, 2017

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