Question 174263: 1. find the x and y intercepts for 6x-4y=12
2. find the equation of a line that contains the point (0,2) and has a slope -3.
3. find the equation of a line that contains the point(1,0) and has a slope of 2.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first two to get you started
# 1
x-intercept
To find the x-intercept, plug in  and solve for x
 Start with the given equation.
 Plug in .
 Multiply  and 0 to get 0.
 Simplify.
 Divide both sides by  to isolate  .
 Reduce.
So the x-intercept is ) .
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y-intercept
To find the y-intercept, plug in  and solve for y
Start with the given equation.
 Plug in .
 Multiply and 0 to get 0.
 Simplify.
 Divide both sides by to isolate  .
 Reduce.
So the y-intercept is ) .
# 2
If you want to find the equation of line with a given a slope of  which goes through the point ( , ), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
 where  is the slope, and ) is the given point
So lets use the Point-Slope Formula to find the equation of the line
 Plug in  ,  , and  (these values are given)
 Distribute
 Multiply and  to get
 Add 2 to both sides to isolate y
 Combine like terms and to get
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Answer:
So the equation of the line with a slope of which goes through the point (,) is:
which is now in  form where the slope is and the y-intercept is 
Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver)
 Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
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