Question

Express y in terms of x for the equation 3x-4y+7=0. Check weather the points (-3,4) and (0,7/4) lie on the graph of this equation or not.

Answer 1

3x -4y +7 = 0

3x + 7 = 4y

4y = (3x +7)

y = (3x +7)/4 -----------(1)

hence, y = (3x +7)/4 is y in term of x.

now,
( -3, 4) it means x = -3 and y = 0
put x = -3 in equation (1)

y = { 3×(-3)+7}/4 = (-9+7)/4 = -1/2
but y = 4
so, ( -3, 4) is not present in 3x -4y +7 =0

checking of ( 0 , 7/4)
means x = 0 and y = 7/4
put x = 0 In equation (1)

y = (3×0+7)/4 = 7/4
also given y = 7/4
so, ( 0 , 7/4) present in equation 3x -4y +7=0

Answer 2

3x - 4y + 7=0

- 4 y + 7 = - 3x

- 4 y = -3x - 7

y = $\frac{-3x - 7}{-4}$

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( -3 ,4)

3x - 4y + 7 = 0

x = - 3

y = 4

3 × - 3 - 4 × 4 + 7

= (- 9 ) - 16 + 7
= -18 ≠ 0

So ,
( -3 , 4 ) is does not lie on the graph of the equation
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(0 , $\frac{7}{4} }$ )

3x - 4y + 7 = 0

= 3 × 0 - 4 × $\frac{7}{4} }$ + 7

= 0 - 7 +7

= -7 + 7 = 0

SO ,
(0,$\frac{7}{4} }$) lie on the graph of the equation.