Question

Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.

Answer 1

y = 2x + 4.

Explanation:

The slope = the slope of y = 2x - 3 which is 2.

Using the point-slope form:

y - y1 = 2(x - x1)

Using the point (-1, 2):

y - 2 = 2(x - -1)

y = 2x + 2 + 2

y = 2x + 4 is the answer.

Answer 2

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

`y = mx + b`

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be
`m = 2.`

`y = 2x + b`

We substitute the given point to find b:

`2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4`

Finally the line is:

`y = 2x + 4`

Answer:

`y = 2x + 4`