Question

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

Answer 1

Answer:

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 = $\frac{3}{4}$ x + $\frac{5}{4}$ ← in slope- intercept form

with slope m = $\frac{3}{4}$

Parallel lines have equal slopes

Consider the given equations

A

y = 3x + 5 ⇒ m = 1 ← not parallel

B

4y = 3x - 1 ⇒ m = $\frac{3}{4}$ ← parallel

C

3y = 4x + 5 ⇒ m = $\frac{4}{3}$ ← not parallel

D

- 4y = 3x + 5 ⇒ m = - $\frac{3}{4}$ ← not parallel

E

4y = x + 5 ⇒ m = $\frac{1}{4}$ ← not parallel

The only line parallel to the given line is B

Answer 2

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

 Equation of the line given in the question is,

• 4y = 3x + 5

Convert the equation into slope-intercept form,

$y=\frac{3}{4}x+\frac{5}{4}$

Slope of the line = $\frac{3}{4}$

y-intercept of the line = $\frac{5}{4}$

Property of two parallel lines,

If two lines having slopes $m_1$ and $m_2$ are parallel,

• $m_1=m_2$

Therefore, all the lines having slope $\frac{3}{4}$ 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

$y=\frac{3}{4}x-\frac{1}{4}$

Slope of the line = $\frac{3}{4}$

Option C

Equation of the line → 3y = 4x + 5

$y=\frac{4}{3}x+\frac{5}{3}$

Slope of the line = $\frac{4}{3}$

Option D

Equation of the line → -4y = 3x + 5

$y=\frac{-3}{4}x-\frac{5}{4}$

Slope of the line = $-\frac{3}{4}$

Option E

Equation of the line → 4y = x + 5

$y=\frac{1}{4}x+\frac{5}{4}$

Slope of the line = $\frac{1}{4}$

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

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