## A line is given by the equation 3x + 2y = 4. What is the equation of a line parallel to the given line and passing through the point (6, -3)

Question

A line is given by the equation 3x + 2y = 4. What is the equation of a line parallel to the given line and passing through the point (6, -3)?

Question 13 options:

A. 3x + 2y = 24
B. 3x+ 2y = 12
C. 2x – 3y = 21
D. 2x – 3y = 3

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2 weeks 2021-09-15T01:12:24+00:00 1 Answer 0

1. Answer: B. 3x+ 2y = 12

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m represents the slope of the line.

c represents the y intercept

The equation of the given line is

3x + 2y = 4

2y = -3x + 4

Dividing through by 2, it becomes

y = – 3x/2 + 2

Comparing with the slope intercept form, slope = – 3/2

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (6, – 3) is – 3/2

To determine the y intercept, we would substitute m = – 3/2, x = 6 and y = -3 into y = mx + c. It becomes

– 3 = – 3/2 × 6 + c

– 3 = – 9 + c

c = – 3 + 9

c = 6

The equation becomes

y = -3x/2 + 6

Cross multiplying by 2, it becomes

2y = – 3x + 12

3x + 2y = 12