Question

5. A line is constructed such that the x-intercept of the line is at the point (-3d,0) and the y-intercept is at the point(0,d). Write an equation for the line q, in terms of x, y and d, that is true for all real values of d.

Answer 1

For this case we need to take in count that the equation of a line is given by:

`y=mx+b`

Where m is the slope and b the intercept. We can find the slope with this formula:

`m=(d-0)/(0-(-3d))=(d)/(3d)=(1)/(3)`

Now we just need to find the intercept. And we can use one point given and we got:

`d=(1)/(3)(0)+b`

So then our equation would be:

`y=(1)/(3)x+d`

And we can verify that it works

x=-3d y= 1/3 (-3d)+d= -d+d=0

x=0 y= 1/3 (0) +d =d