Question

How to determine the equation of the line parallel to 3x - 2y + 4 = 0 and passing through (1,6)?

Answer 1

Answer:

Step-by-step explanation:

y - 6 = 3(x - 1) / 2

OR

3x - 2y + 9 = 0.

Answer 2

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The equation of a line in slope-intercept form is.

y=mx+b

where m represents the slope and b, the y-intercept.

Rearrange 3x−2y+4=0 into this form

add 2y to both sides.

3x−2y+2y+4=0+2y

⇒2y=3x+4

divide ALL terms on both sides by 2

2y2=32x+42

⇒y=32x+2← in form y=mx+b

⇒slope =m=32

The equation of a line in point-slope form is.

y−y1=m(x−x1)

m is slope and (x1,y1) a point on the line

For parallel line m=32 and (x1,y1)=(1,6)

⇒y−6=32(x−1)← in point-slope form

Distributing the bracket and simplifying gives the equation in an alternative form.

y−6=32x−32

⇒y=32x−32+6

⇒y=32x+92← in slope-intercept form

graph{(y-3/2x-2)(y-3/2x-9/2)=0 [-10, 10, -5, 5]}