Question

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

Answer 1

Answer:

y = (-3/2)x + 7

Step-by-step explanation:

3x + 2y = -4 (rearrange to slope intercept form y = mx + b)

2y = -3x - 4

y = (-3/2) x - 2

comparing this to the general form of a linear equation : y = mx + b

we see that slope of this line (and every line that is parallel to this line),

m = -3/2

if we sub this back in to the general form, we get:

y = (-3/2)x + b

We are still missing the value of b. To find this, we are given that the point (4,1) lies on the line. We simply substitute this back into the equation and solve for b.

1 = (-3/2)4 + b

1 = -6 + b

b = 7

substituting this back into the equation:

y = (-3/2)x + 7

Answer 2

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