Question

In standard form, write an equation for the line that passes through (–2, –5) and is parallel to the line 15x − 5y = 10.

Answer 1

Anything parallel to Ax+By = C will be of the form Ax+By = D
The only difference is the C has been replaced with D.

For example,
2x+3y = 5 is parallel to 2x+3y = 7
Both equations have a slope of -2/3. Parallel lines have equal slopes but different y intercepts.

Answer 2

In the case of 15x − 5y = 10, we see that A = 15, B = -5 and C = 10
Anything parallel to this will be 15x - 5y = D
To find the value of D, plug in (x,y) = (-2, -5), which is the point we want the parallel line to go through. Simplify to calculate D.

Answer 3

@jimthompson5910 Thank you, this helped! :)

Answer 4

You're welcome. Let me know what you get for that D value.

Answer 5

@jimthompson5910 I got −5≠10, which is false.

Answer 6

No, it's a good thing you didn't get 10 as a result. This is because the y intercepts are different for the parallel equations. D = -5 is correct.

The equation 15x - 5y = -5 is parallel to 15x-5y = 10
The point (-2, -5) is on 15x - 5y = -5

Answer 7

If you wanted, you can solve each for y
15x - 5y = -5
-5y = -15x - 5
y = (-15x-5)/(-5)
y = (-15x)/(-5) - 5/(-5)
y = 3x + 1


Similarly
15x - 5y = 10
-5y = -15x + 10
y = (-15x+10)/(-5)
y = (-15x)/(-5) +10/(-5)
y = 3x - 2

Both equations have a slope of m = 3, but different y intercepts (b = 1 and b = -2 respectively)

Answer 8

@jimthompson5910 I was confused with this question for hours, thank you. <3

Answer 9

You're welcome