Question

Find the equation of the line parallel to 6x+5y=1 and passing through (-4,-2)

Answer 1

Hi Student!

The first step that we need to take before trying to solve the problem is that we need to take out important information from the problem. The first important piece of information that is given to us is that we are trying to find an equation of a line that is parallel to a different line. This means that our slope is going to be the same as the initial line given. The second piece of information that is given is a point through which our line passes through which will help us greatly when solving for our line.

The next step that we must take is to solve for y in the given equation so we can see what the slope is.

Subtract 6x from both sides

• 
  `6x + 5y = 1`

• 
  `6x - 6x + 5y = 1 - 6x`

• 
  `5y = 1 - 6x`

Divide both sides by 5

• 
  `(5y)/(5) = (1 - 6x)/(5)`

• 
  `y= (1)/(5) - (6x)/(5)`

• 
  `y=- 1.2x+ 0.2`

Now that we have completely solved for y, we can see that the slope is -1.2 using the y = mx + b formula which states that m is the slope.

Moving onto the next step, we must use the point-slope formula to determine what the new equation is that has the same slope and passes through (-4, -2).

Insert the Values

• 
  `(y-y_1)=m(x-x_1)`

• 
  `(y-(-2))=-1.2(x-(-4))`

Simplify the Equation

• 
  `y+2=-1.2(x+4)`

Distribute the Equation

• 
  `y+2=(-1.2*x)+(-1.2*4)`

• 
  `y+2=-1.2x-4.8`

Subtract 2 from both sides (to isolate y)

• 
  `y+2 - 2=-1.2x-4.8- 2`

• 
  `y=-1.2x-6.8`

Therefore, our final answer for the equation of the line parallel to 6x + 5y = 1 and that passes through (-4, -2) is y = -1.2x - 6.8.