Question

Which of these points lie on the line $7x+8y=61$?

• A. (2, 5)
• B. (3, 4)
• C. (-3, 7)
• D. (3, 5)

Answer 1

The correct option is D

(3, 5)

Each point (x, y) on a line representing the linear equation ax + by + c = 0, is a solution of the linear equation.

$\Rightarrow$ The given point lie on the line representing the equation if it satisfies the equation.

Substituting the value of x = 3 and y = 4,
$7x+8y=61$ = $7\left(3\right)+8\left(4\right)=53$.

Substituting the value of x = 2 and y = 5,
$7x+8y=61$ = $7\left(2\right)+8\left(5\right)=54$.

Substituting the value of x = -3 and y = 7,
$7x+8y=61$ = $7(-3)+8\left(7\right)=35$.

Substituting the value of x = 3 and y = 5,
$7x+8y=61$ = $7\left(3\right)+8\left(5\right)=61$

Hence, (3,5) lies on the line represented by the given equation.