Which equation of the straight line is parallel to 4y=3x+5

   Line given in option B will be parallel to the line 4y = 3x + 5.

 Equation of the line given in the question is,

Convert the equation into slope-intercept form,

Slope of the line =

y-intercept of the line =

Property of two parallel lines,

If two lines having slopes and are parallel,

Therefore, all the lines having slope will be parallel to the given line "4y = 3x + 5".

Option A

Equation of the line → y = 3x + 5

Slope of the line = 3

Option B

Equation of the line → 4y = 3x - 1

Slope of the line =

Option C

Equation of the line → 3y = 4x + 5

Slope of the line =

Option D

Equation of the line → -4y = 3x + 5

Slope of the line =

Option E

Equation of the line → 4y = x + 5

Slope of the line =

  Therefore, line given in Option B will be parallel to the line having equation "4y = 3x + 5".

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B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4y = 3x + 5 ( divide all terms by 4 )

y = x + ← in slope- intercept form

with slope m =

Parallel lines have equal slopes

Consider the given equations

A

y = 3x + 5 ⇒ m = 1 ← not parallel

B

4y = 3x - 1 ⇒ m = ← parallel

C

3y = 4x + 5 ⇒ m = ← not parallel

D

- 4y = 3x + 5 ⇒ m = - ← not parallel

E

4y = x + 5 ⇒ m = ← not parallel

The only line parallel to the given line is B