Question

Write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation.

(-1,3);y = 2x - 8

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 is the slope of the line

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

We have the following line:

`y = 2x-8`

The slope is
`m_ {1} = 2`

By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to the given line will have a slope
`m_ {2} = 2`

Therefore, the equation of the parallel line will be of the form:

`y = 2x + b`

We substitute the given point and find "b":

`3 = 2 (-1) + b\\3 = -2 + b\\3 + 2 = b\\b = 5`

Finally, the equation is:

`y = 2x + 5`

Answer:

`y = 2x + 5`