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find the slope of line passing through the point (3,4) and (8,-3)

Guest Jul 31, 2017
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Before attempting to do this problem, you must understand the slope-intercept form of a line. It is the following:
 

\(y=mx+b\)

m = slope of the line

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

 

First, we must find the slope. To do this, we must know another formula. This will solve for m.

 

\(m=\frac{y_2-y_1}{x_2-x_1}\)

 

Now that we know the formula, let's plug the given coordinates into the formula above to determine the line's slope:

\(m=\frac{y_2-y_1}{x_2-x_1}\) Plug in the coordinate given into this formula to find the slope of the line, 
\(m=\frac{4-(-3)}{3-8}\) Remember that subtracting a negative is the same as adding a positive.
\(m=\frac{4+3}{3-8}\) Now, simplify the numerator and denominator into its simplest terms.
\(m=\frac{7}{-5}=-\frac{7}{5}\)  
   

 

We have now determined the slope of the line, -7/5. The next step is to figure out the value of b. First, let's look at the equation with the m filled in.

 

\(y=-\frac{7}{5}x+b\)

 

Just plug in a coordinate into here and solve for b. It doesn't matter which coordinate you substitute in, either. I'll use the first point, (3,4):

 

\(y=-\frac{7}{5}x+b\) Plug in the coordinate (3,4) into the equation and solve for b.
\(4=-\frac{7}{5}*3+b\) First, let's simplify the right hand side of the equation by doing -7/5*3
\(-\frac{7}{5}*3=\frac{-7}{5}*\frac{3}{1}=\frac{-21}{5}=-\frac{21}{5}\) Plug this back into the equation we were solving.
\(4=-\frac{21}{5}+b\) Multiply 5 on both sides of the equation to get rid of the pesky fractions.
\(20=-21+5b\) Add 21 to both sides of the equation.
\(41=5b\) Divide by 5 on both sides.
\(\frac{41}{5}=b\)  
   

 

Now that we have both and solved, we can write the equation in slope intercept form. 

 

\(y=mx+b\)

 

Just replace and with the numbers we calculated for both. Therefore, your final answer is:
 

\(y=-\frac{5}{7}x+\frac{41}{5}\) 

 

Here, I have supplied a link to an online graphing calculator called Desmos. It shows you that this is indeed the line that passes through both points. Here is the link: https://www.desmos.com/calculator/0tjwjbb3e7

TheXSquaredFactor  Jul 31, 2017

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