What is an equation of the line that passes through the point (-5,7)(−5,7) and is parallel to the line x-5y=15x−5y=15?

Answer 1

Hi Oliviah L

If the line is

x - 5y = 15

and the coordinates are (-5,7)

Then a parallel line would have exactly the same slope and you can use the coordinates given to solve for b.

-5y = - x + 15

Solve for y to get this in Slope Intercept Form

y = (1/5)x - 3

The slope of the parallel line, is (1/5)

y = (1/5)x + b

Use the coordinates given to solve for b

7 = (1/5)(-5) + b

7 = -1 + b

7 + 1 = b

8 = b

The parallel line is

y = (1/5)x + 8

You can graph both lines at Desmos.com to confirm that they are parallel. I hope this help and please let me know if the information about the line and the coordinates is correct.

Answer 2

IF the line is 15x -5y = 15

divide by 5 to get

3x -y = 3

solve for y

y =3x -3 which has slope = 3. if a linear equatiion is solved for y, the slope = the coefficient of the x term. Then Any parallel line has the same slope

y=3x + b, to solve for b plug in the point (-5,7) with x=-5, y=7

7 = 3(-5) + b

b = 7+15 = 22

y= 3x +22 is the parallel line through the point (-5,7)