Write and equation of the line parallel to the line  2 x + 4 y = 20 2 x + 4 y = 20 and containing the point  ( − 6 , 3 ) ( - 6 , 3 ) Write

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

2x + 4y = 20

4y = - 2x + 20

Dividing through by 4, it becomes

y = - x/2 + 5

Comparing with the slope intercept form, slope = - 1/2

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 6, 3) is - 1/2

To determine the y intercept, we would substitute m = - 1/2, x = - 6 and y = 3 into y = mx + c. It becomes

3 = - 1/2 × - 6 + c

3 = 3 + c

c = 3 - 3 = 0

The equation becomes

y = - x/2