Question

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

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

Answer 1

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

Answer 2

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.