Question

Write an equation in slope-intercept

form to represent the line parallel to
3x - y = 5 passing through the point
(-1,-2).

Answer 1

For this case we have that, by definition, the equation of a line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

On the other hand, we have that if two lines are parallel then their slopes are equal.

We have the following equation of the line:

`3x-y = 5`

Rewriting we have:

`y = 3x-5`

Thus, the slope of the lines is
`m_ {1} = 3`

Then, a parallel line will have slope
`m_ {2} = 3`

Thus, the equation of the new line will be given by:

`y = 3x + b`

To find the cut-off point "b", we substitute the point through which the line passes:

`-2 = 3 (-1) + b\\-2 = -3 + b\\-2 + 3 = b\\b = 1`

Finally the equation is:

`y = 3x + 1`

ANswer:

`y = 3x + 1`