Question

P, Q, R, and S are four friends located at different places of the city. What is the equation for the friends who are farthest away from each other?

• A. y = 2x - 30
• B. y = 2x + 20
• C. y = 3x - 20
• D. y = 3x + 20

Answer 1

The correct option is D y = 3x + 20

From the graph, we can see that P and S are farthest away from each other.

$\therefore$ Slope, m = $\frac{\Delta y}{\Delta x}$

= $\frac{200-50}{60-10}$

= $\frac{150}{50}$

= 3

We know that equation of a line is
y = mx + c

y = 3x + c --------> (1)

Substitute one of the coordinates, say (10,50) in the equation (1), we get,

50 = 3(10) + c

$⟹$ 50 = 30 + c

$⟹$ 50 - 30 = c

$⟹$ 20 = c

Hence, the required equation is
y = 3x + 20.