+0  
 
0
32
1
avatar

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

Guest Jul 31, 2017
Sort: 

1+0 Answers

 #1
avatar+808 
0

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

9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details