SOLUTION: 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

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

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