Write the equation of a line that is perpendicular to y= 2/3x + 3 and passes through the point (4, -8).
Mathematics · High School · Mon Jan 18 2021
Answered on
Given the points:
(4, -8)
x1 = 4
y1 = -8
Perpendicular to y = ⅔x + 3
Perpendicular means that they have the same slope. The given line is written in slope-intercept form, y = mx + b, whereas m is considered to be the slope of the line.
m = ⅔
Solution:
In order to determine the equation of the line we can both write in point-slope form, and slope-intercept form.
Point-slope form: y - y1 = m (x - x1)
y - (-8) = ⅔( x - 4)
y + 8 = ⅔(x - 4)
In order to change the given equation to slope-intercept form, we distribute ⅔ to the values inside the parenthesis, and then transpose 8 to the other side of the equation, hence we must take note that in transposing a number, the sign changes.
y + 8 = ⅔x - 8/3
y = ⅔x - 8/3 -8
8 can be written as 24/3
y = ⅔x - 8/3 - 24/3
y = ⅔x - 32 / 3
Final answer:
y = ⅔x - 32 / 3