Finding an equation parallel to given line with specific points

Question

Find the equation of the line that is parallel to the given line and passes thru given points. 3x-2y=9 points (-3,-1)

Answer 1

Parallel lines have the same slope.

 

The equation is given in Standard Form (Ax+By=C) and the slope, m=(-A/B).

 

The parallel line has the equation: 3x -2y = C   and we need point (-3,-1) to determine C.

     3(-3) - 2(-1) = C

      -9 + 2 = C

       -7 = C

 

The equation of the parallel line, in Standard Format, is:   3x - 2y = -7

Answer 2

Parallel line have equal slopes

 

Let's find the slope of 3x - 2y = 9

 

To do this, we can write the equation of the above line in slope-intercept form y = mx + b, where m = slope

 

-2y = 9 - 3x

 

y = -9/2 + 3/2 x = 3/2 x - 9/2

 

The slope of this line is 3/2

 

To find the equation of our line, we can use the point slope form

 

y - y₀ = m(x - x₀)

 

(x_0, y₀) is (-3, -1)

 

We have 

 

y + 1 = 3/2 (x + 3)

 

y + 1 = 3/2 x + 9/2

 

y = 3/2 x + 7/2