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Maths-

General

Easy

Question

In the $x y.$ -plane, the point $left parenthesis p comma r right parenthesis$ lies on the line with equation $y equals x plus b$ , where b is a constant. The point with coordinates $left parenthesis 2 p comma 5 r right parenthesis$ lies on the line with equation $y equals 2 x plus b$ . If $p not equal to 0$ , what is the value of $r over p$ ?

$\frac{2}{5}$
$\frac{3}{4}$
$\frac{4}{3}$
$\frac{5}{2}$

hint Hint:

We put the value of x- and y-coordinate in the equations and solve the problem.

The correct answer is: $3 over 4$

Step 1 of 2:
In the x y-plane, the point $left parenthesis p comma r right parenthesis$ lies on the line with equation y = x + b, where b is a constant.
Therefore, putting x = p, we get y = $p plus b$ Hence, r = $p plus b$ $rightwards double arrow$ b= r –p.
Step 2 of 2:
Similarly, for the point with coordinates (2p, 5r) lies on the line with equation y = 2x +b.
Now, putting x = 2p and b = r – p, we get
y = 2(2p) +(r – p)
y = 4p + r – p
y = 3p + r
Now, we have 5r = 3p + r
5r – r = 3p
4r = 3p
$not stretchy rightwards double arrow r over p equals 3 over 4$
Final Answer:
The value of is— B)

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