Having some problem with a problem

[jordan7]

Our prof recently gave this one problem I can't find out how to do.

Line 1 and Line 2 are parallel lines. Line 1 has a=-2 and passes through (3,-1/3). Find the general form of line 2.

So the only given are x intercept of line 1, which is -2 and it passes through a point (3,-1/3).

First thing that came to my mind was to solve for the slope using the given x intercept and the given point. After getting the slope, I am now stuck. How am I supposed to find the parallel line #2 without any given point that it passes through or something. I am really confused, please help.

 

[HallsofIvy]

So "a" is the x- intercept for Line 1? A line in a given two-dimensional coordinate system can be written y= mx+ b for some numbers m and g. If -2 is the x-intercept then y=0 when x= -2. 0= m(-2)+ b so -2m+ b= 0. If Line 1 also passes through (3, -1/3) then when x= 3, y= -1/3 so -1/3= m(3)+ b so 3m+ b= -1/3.

Solve the two equations -3m+ b= 0 and 3m+ b= -1/3 for m. (Do you see that subtracting one equation from the other will immediately eliminate b?)

Now, the problem does NOT ask you to find a unique equation for Line 2! It asks for "the general form of line 2." There are infinitely many lines that are parallel to Line 1. What can you say about all of them?

 

[Deleted member 4993]

Our prof recently gave this one problem I can't find out how to do.

Line 1 and Line 2 are parallel lines. Line 1 has a=-2 and passes through (3,-1/3). Find the general form of line 2.

So the only given are x intercept of line 1, which is -2 and it passes through a point (3,-1/3).

First thing that came to my mind was to solve for the slope using the given x intercept and the given point. After getting the slope, I am now stuck. How am I supposed to find the parallel line #2 without any given point that it passes through or something. I am really confused, please help.

So the only given are x intercept of line 1, which is -2 and it passes through a point (3,-1/3).

x-intercept means y=0 there.

So the line passes through (-2,0) and

the line passes through (3,-1/3)

If a line passes through (x₁,y₁) and (x₂,y₂),

the slope of the line is:

\(\displaystyle m \ = \ \frac{y_2 - y_1}{x_2 - x_1}\)

and the equation of the line is (not really needed here - just for future reference):

\(\displaystyle \frac{y - y_1}{y_2 - y_1} \ = \ \frac{x - x_1}{x_2 - x_1}\)

continue....