Question

Write an equation in slope-intercept

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:

$y = 3x + 1$