What is the equation of the line that is parallel to the given line and passes through the point (-2, 2)? y=1/5x+4 y =1/5x+12/5 y=-5+4 y=-5x12/5

Given:

Points ( -2, 2)

x1 = -2

y1 = 2

The parallel line is not stated, but since from the choices, all the slopes are 1/5 then we can assume that the slope of the line is 1/5.

m = 1/5

Determine the equation of the line.

In order to write the equation of the line, we must first write in point-slope form, then equate to slope-intercept form

Formula for the point-slope form:

y -y1 = m (x - x1)

Formula for the slope-intercept form

y = mx + b


Solution:

Solve for point-slope form first, before going to slope-intercept form.

Substitute the given values of x1, m and y1 to the formula for the point-slope form.

y - 2 = 1/5 ( x -(-2))

y - 2 = 1/5 ( x + 2)

In order to equate to slope-intercept form, we simply need to distribute 1/5 to each value inside the parenthesis, and then transpose -2 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

y - 2 = 1/5 ( x + 2)

y -2 = 1/5x + 2/5

y = 1/5x + 2/5 + 2

2 can be written as 10/5 in order to compute easily.

y = 1/5x + 2/5 + 10/5

y = 1/5x + 12/5

Final answer:

y = 1/5x + 12/5