Write the equation of a line that is parallel to 2y=x-10 passing through (2,1)

Step-by-step explanation:

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

y = mx + c

Where

c represents the y intercept

m represents the slope of the line.

The equation of the given line is

2y = x - 10

Dividing both sides of the equation by 2, 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 (2,1) is 1/2

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

1 = 1/2 * 2 + c

1 = 1 + c

c = 1 - 1 = 0

The equation becomes

y = x/2

the line that is parallel will be y = 1/2x