Answer:
B.) 3 /4 .
Explanation:
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 r / p , we need to divide both sides of the equation by p and by 4:
3p=4r
3 = 4 / r /p
3 /4 = r /p
The correct answer is B.) 3 /4 .
If you picked choices A and D, you may have incorrectly formed your answer out of the coefficients in the point (2p,5r). If you picked Choice C, you may have confused r and p.
Answer:
B
Explanation:
If the point (p, r) lies on y = x + b, then if we plug in p for x and r for y, the equation will hold true. So let's try that:
r = p + b
Now, since the point (2p, 5r) lies on the line y = 2x + b, we can plug 2p in for x and 5r in for y:
5r = 2 * 2p + b
5r = 4p + b
Let's substitute p + b in for r:
5r = 4p + b
5 * (p + b) = 4p + b
5p + 5b = 4p + b
p = -4b
We now have p in terms of b. Let's do the same for r, so plug -4b in for p in
r = p + b:
r = p + b
r = -4b + b
r = -3b
We want to find the value of r/p, so let's right this in terms of b:
r/p
-3b/-4b
The b's and negative signs will cancel out, so we're left with 3/4.
The answer is B.
Hope this helps!
