write an equation of the line parallel to x+2y=-4 through the point (-8,5) show all work

Given:

Points ( -8, 5 )

x1 = -8

y1 = 5

Parallel to x + 2y = -4 or y = -½x - 2

Parallel, means they have same slope

m = -½

Write the equation of the line.

The equation of the line can be written in slope-intercept form, and point-slope 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 - 5 = -½ ( x - (-8) )

y - 5 = -½ ( x + 8 )

In order to equate to slope-intercept form, we simply need to distribute -½ to each value inside the parenthesis, and then transpose -5 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

y - 5 = -½ ( x + 8 )

y - 5 = -½x - 4

y = -½x - 4 + 5

y = -½x + 1

Final answer:

y = -½x + 1