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4x + 5y + 6 = 0

Guest Jul 28, 2017
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To determine the intercepts of this equation in the form \(ax+by+c=0\), I would just make x and y zero and see what the result is:
 

Finding the x-intercept

 

For a line without the slope of 0, the line only touches the x-axis once. For a point to be on the x-intercept, y must be zero; otherwise, it would not be on the x-intercept. Knowing this, you can set the y to be zero and solve for x:

 

\(4x+5y+6=0\) Make y=0 so that the point is on the x-intercept.
\(4x+5*0+6=0\)  
\(4x+6=0\) Subtract 6 on both sides.
\(4x=-6\) Divide by 4 on both sides.
\(x=\frac{-6}{4}=-\frac{3}{2}=-1.5\)  
   

 

Ok, we have determined that the x-intercept is located exactly on the point \((-\frac{3}{2},0)\)

 

Finding the y-intercept

 

You will utilize the exact same logic to find the y-intercept. Of course, x will be equal to 0 this time:
 

\(4x+5y+6=0\) Substitute 0 in for x.
\(4*0+5y+6=0\)  
\(5y+6=0\) Subtract 6 on both sides.
\(5y=-6\) Divide by 5 on both sides.
\(y=-\frac{6}{5}=-1.2\)  
   

 

Ok, we have determined that the y-intercept is located exactly on the point \((0,-1.2)\).

 

You actually do not need any more information to graph this equation. Plot both the intercepts on a coordinate plane, and use a ruler to connect them. Then, you are done!

TheXSquaredFactor  Jul 28, 2017

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