Question is in description.

Question

Find the equation for the line that passes through the point (−3, −3), and that is parallel to the line with the equation −3/2x + 2y = 17/2.

Answer 1

Line:

     −3/2x + 2y = 17/2

is the same as line:

       3x  - 4y = -17             [multiply by (-2); this is Standard Format (Ax+By=C)]

 

All parallel lines have the same slope (-A/B), so the parallel line has the formula:

       3x  - 4y = D            [and we need point (-3,-3) to determine D]

    3(-3) - 4(-3) = D

      -9 + 12 = D

         D = 3

 

So, the equation of the parallel line (in Standard Form) is:

      3x - 4y = 3

Answer 2

Hello Shatoria,

 

The equation you have is -3/2x + 2y = 17/2

 

Let's solve this for y in terms of x

 

2y = 3/2 x + 17/2

y = 3/4x + 17/4

 

This tells us the slope of the line is 3/4.

 

Now parallel lines have the same slope.

 

Using the point slope form of an equation for a line

y-y₁ = m(x-x₁) and the point (-3,-3)

 

we have

y-(-3) = (3/4)[x-(-3)]

y+3 = (3/4)(x+3)

y+3 = 3/4 x + 9/4

y = 3/4 x - 3/4