What is an equation of the line that passes through the point (-8,-7) and is parallel to the line x-2y=12 ?

Given:

Points ( -8, -7 )

x1 = -8

y1 = -7

Parallel to 2y = -x + 12
y = -½x + 6

Parallel, means they have same slope

m = -½

Write the equation of the line in slope-intercept form.

Before writing in slope-intercept form, we must first write in 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 - (-7) = -½ ( x - ( -8)

y + 7 = -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 7 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

y + 7 = -½x - 4

y= -½x - 4 - 7

y = -½x - 11

Final answer:

y = -½x - 11