Question

What is the equation of the line parallel to 3x+2y= -4 that goes through the point (4,-1)

Answer 1

Answer:

2y + 3x = 10

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 )

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = - $\frac{3}{2}$ x - 2 ← in slope- intercept form

with slope m = - $\frac{3}{2}$

• Parallel lines have equal slopes, thus

y = - $\frac{3}{2}$ x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - $\frac{3}{2}$ x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form

Answer 2

The equation of the line parallel to 3x+2y= -4 goes through the point (4,-1).

• 3x + 2y = 10 ← in standard form.
• y = -  x + 5 ← in slope- intercept form

Equation of line

The general equation of a straight line exists y = mx + c, where m is the gradient, and y = c exists the value where the line cuts the y-axis. This number c is named the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis stands y = mx + c.

The equation of a line in slope- intercept form is

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

Rearrange 3x + 2y = - 4 into this form

Subtract 3x from both sides

2y = - 3x - 4 ( divide all terms by 2 )

y = -  x - 2 ← in slope- intercept form

with slope m = -

• Parallel lines have equal slopes, thus

y = -  x + c ← partial equation of parallel line

To find c substitute (4, - 1) into the partial equation

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = -  x + 5 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 10 ( add 3x to both sides )

3x + 2y = 10 ← in standard form.

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