Question

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

• A. $(1,1)$
• B. $(0,\frac{7}{4})$
• C. $(0,7)$
• D. $(\frac{7}{3},0)$

Answer 1

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

The correct options are
A

$(1,1)$

B

$(0,\frac{7}{4})$

D

$(\frac{7}{3},0)$

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 of the equation.

Let's substitute the points given in the options in 3x + 4y = 7 to check which of them satisfy the equation.

$(1,1):$
$LHS=3x+4y=3\times \left(1\right)+4\times \left(1\right)=7=RHS$

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

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

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

$\therefore$ Points $(1,1),(0,\frac{7}{4})and(\frac{7}{3},0)$ lie on the given line.