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ROJoin ‼️
Since the point (p,r) lies on the line with equation y=x+b, the point must satisfy the equation. Substituting p for x and r for y in the equation y=x+b gives r=p+b, or b = r−p.
Similarly, since the point (2p,5r) lies on the line with the equation y=2x+b, the point must satisfy the equation. Substituting 2p for x and 5r for y in the equation y=2x+b gives:
5r=2(2p)+b
5r=4p+b
b = 5r−4p.
Next, we can set the two equations equal to b equal to each other and simplify:
b=r−p=5r−4p
3p=4r
Finally, to find rp, we need to divide both sides of the equation by p and by 4:
3p=4r
3=4rp
34=rp
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