(0,0);y=2/3x+1

Question

write and equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation

Answer 1

Hello Connie,

 

For two lines to be parallel, they must have the same slope. The slope is the number that multiplies "x" in the equation. Therefore, for the given equation of

 

  y = (2/3)x + 1

 

the slope is 2/3. Thus, the equation we want is of the form

 

  y = (2/3)x + B

 

where B is the unknown intercept (place where the line crosses the y-axis). Now let's use the second piece of information we are given -- the line passes through the given point of (x=0, y=0). With our equation of the form y=(2/3)x + B, then substituting x=0 and y=0, we are left with

 

  0 = (2/3)0 + B

 

so B must be 0.

 

Putting it all together then, our equation that is parallel and through (0,0) is

 

  y = (2/3)x + 0, or simply y = (2/3)x

 

Note that I put the () around the 2/3 just to make it clear; you don't have to have them, we could write

 

  y = 2/3x

 

because even without the (), you still divide 2 by 3 first, then multiply by x.

 

Hope this is clear for you.