What is an equation of the line that passes through the point ( − 5 , − 1 ) (−5,−1) and is parallel to the line 4 x − 5 y = 10 4x−5y=10?

Step-by-step explanation:

The equation of a straight line is expressed in the slope intercept form as

y = mx + c

Where m represents the slope

c represents the intercept.

The given equation is

4x−5y = 10

5y = 4x - 10

y = 4x/5 - 2

Comparing with the slope intercept form,

The slope,m = 4/5

The line that is parallel to the given line passes through the point (- 5,- 1)

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line that is parallel to the given line is 4/5

To determine the intercept c, we will substitute m = 4/5, x = - 1 and x = - 5 into the slope intercept equation. It becomes

- 5 = 4/5 × - 1 + c

- 5 = - 4/5 + c

c = - 5 + 4/5 = (- 25 + 4)/5 = - 21/5

The equation becomes

y = 4x/5 - 21/5

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