Write the standard form of the equation of the line described.

Question

through: (2,-5), parallel to y=4x+5

Answer 1

The Standard Form of the equation of a line looks like :   Ax + By = C
   [ note: the slope is (-A/B) ]
 
First, convert the given equation into Standard Form:
                      y = 4x + 5
                    -4x + y = 5      (subtract 4x from both sides)
                     4x -y = -5   
        (note:  it is preferred that the coefficient of x be positive, so multiply by -1)
 
Parallel lines have the same slope, so the equation of the line described is:
                     4x - y = D     (note: given equation in Standard Form; D≠C))
          (another note:  coefficient of x is made positive, preferably without fractions)
 
Use point (2,-5) to determine D.
        4(2) - (-5) = D
         8 + 5 = D
            13 = D
 
The equation of the parallel line (in Standard Form) is:    4x - y = 13
 

Answer 2

If the two lines are parallel, how do their slopes compare? Are they the same or different?

What is the slope of the parallel line?

Now that we have the slope, write the equation for the line in point-slope form.

(y-y1) = m * (x-x1)

Distribute the slope then solve for y. Good luck!