Question 243670: Hi, I need help with these two problem.
1. Find an equation of the line meeting the specified conditions. Slope intercepts form containing the point (0,6) and parallel to y=4x-6
2. Find an equation in point slope form of the line having the specified slope and containing the point indicated m=-8;(6,9)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 1
We can see that the equation  has a slope  and a y-intercept  .
Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is .
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point ) .
 Start with the point slope formula
 Plug in ,  , and 
 Distribute
 Multiply
 Add 6 to both sides.
 Combine like terms.
So the equation of the line parallel to that goes through the point is .
Here's a graph to visually verify our answer:
Graph of the original equation (red) and the parallel line (green) through the point .
# 2
If you want to find the equation of line with a given a slope of  which goes through the point (6,9), 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)
Now if you just want the equation in point slope form, then the answer is simply . However, if you want it in slope-intercept form, then read on...
 Distribute
 Multiply and  to get 
 Add 9 to both sides to isolate y
 Add
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line with a slope of which goes through the point (6,9) is:
which is now in  form where the slope is and the y-intercept is 
|
|
|
