|
Question 154564: How would I write these in standard form?
Has a slope of 3 and has a y-intercept of 4
Passes through the points (2,-6) and (4,-6)
Thanks
ryan
Found 2 solutions by checkley77, jim_thompson5910:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! Y=mX+B (red line)
Y=3X+4 THIS LINE HAS A SLOPE=3 & A Y INTERCEPT=4.
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 3x +4 and y = -6).
----------------------------------------
slope=(-6+6)/4-2)=0/2 represents a horizontal line through -6 (green line).
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! # 1
Since the equation has a y-intercept of 4, this means that the line goes through the point (0,4)
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 4 to both sides to isolate y
 Add and to get
------------------------------------------------------------------------------------------------------------
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.
# 2
First let's find the slope of the line through the points ) and )
 Start with the slope formula.
 Plug in  ,  ,  , and 
 Subtract  from to get
 Subtract  from to get
 Reduce
So the slope of the line that goes through the points and is
Now let's use the point slope formula:
Start with the point slope formula
 Plug in , , and
 Rewrite  as 
 Distribute
 Multiply
 Subtract 6 from both sides.
 Combine like terms.
 Simplify
So the equation that goes through the points and is
Notice how the graph of goes through the points and . So this visually verifies our answer.
 Graph of through the points and
|
|
|
| |
