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:

$m=\frac{d-0}{0-(-3d)}=\frac{d}{3d}=\frac{1}{3}$

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

$d=\frac{1}{3}(0)+b$

So then our equation would be:

$y=\frac{1}{3}x+d$

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