Question

Identify the points which lie on the line 3x + 4y = 7.

• A. 3x - 2y = 5
• B. 2x + y = 17
• C. x + 2y = 17
• D. x - 2y = 4

Answer 1

Answer: (A), (B), (D)

The correct options are
A

3x - 2y = 5

B

2x + y = 17

D

x - 2y = 4

If a point lies on a line, the coordinates should satisfy the equation of the line. So any point lying on the line 3x + 4y = 7 is a solution.
Let's substitute the points given in the options in 3x + 4y = 7 to check which of them satisfy the equation.
$(1,1):$
$3x+4y=7\Rightarrow 3\times \left(1\right)+4\times \left(1\right)=7=RHS$

$(0,\frac{7}{4}):$
$3x+4y=7\Rightarrow 3\times \left(0\right)+4\times \left(\frac{7}{4}\right)=7=RHS$

$(0,7):$
$3x+4y=7\Rightarrow 3\times \left(0\right)+4\times \left(7\right)=28\ne RHS$

$(\frac{7}{3},0):$
$3x+4y=7\Rightarrow 3\times \left(\frac{7}{3}\right)+4\times \left(0\right)=7=RHS$