160k views
2 votes
Which equation represents a line parallel to the line whose equations is -2x + 3y =

-4 and passes through the point (1,3)?

Which equation represents a line parallel to the line whose equations is -2x + 3y-example-1

2 Answers

3 votes

Answer:

2

Explanation:

parallel lines have same slope with different intercept

y= mx+b

m is going to be same with different b

so the given function is:

  • -2x+3y=-4
  • 3y= 2x-4
  • y= 2/3x - 4/3

Given options:

1. y-3= - 2/3(x-1) ⇒ y= -2/3x +3 + 2/3 ⇒ y= -2/3x +11/3

  • it has different slope, so is not parallel

2. y-3= 2/3(x-1) ⇒ y= 2/3x+3-2/3 ⇒ y= 2/3x + 7/3

  • it has same slope, so is parallel
  • it should be passing through point (1,3)
  • 3= 2/3+7/3 ⇒ 3=3, yes it does

3. y-3= -2/3(x+1) ⇒ y= - 2/3x +3- 2/3 ⇒ y= -2/3x + 7/3

  • it has different slope, is not parallel

4. y-3= 2/3(x+1) ⇒ y= 2/3x +3+ 2/3 ⇒ y= 2/3x +11/3

  • it has same slope, so is parallel
  • it should be passing through point (1,3)
  • 3= 2/3+11/3 ⇒ 3≠13/3, no it doesn't
User Psyche
by
7.9k points
0 votes

Answer:

2. y - 3 = 2/3 (x - 1).

Explanation:

-2x + 3y = -4

3y = 2x - 4

y = 2/3 x - 4/3 - so the slope is 2/3.

The slope of a line parallel to it is also 2/3.

It also passes through the point (1, 3).

Using the point-slope form of a line:

y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line, we have:

y - 3 = 2/3 (x - 1) <--- is the required equation.

User Josephus
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories