Which of the following is an equation of the line through (2, 3) and (−1, −12)?
Mathematics · College · Tue Nov 03 2020
Answered on
Given:
(2,3)
(-1,-12)
x1 = 2
x2 = -1
y1 = 3
y2 = -12
Find the equation of the line.
The equation of the line can be represented in slope-intercept form:
y = mx + b
Solution:
Find first the slope of the line.
Slope formula:
m = change in y / change in x
m = (y2 - y1) / (x2 - x1)
m = ( -12 -3) / (-1 -2)
m = -15/-3
m = 5
Equate the given values of x1, y1, and m on the point slope formula. The point slope formula can later be change into slope-intercept form
(y - y1) = m (x - x1)
(y - (-12)) = 5 ( x - 2)
(y + 12) = 5x - 10
transpose 12 on the other side of the equation, note that when transposing a number, the sign changes.
y = 5x - 10 - 12
y = 5x - 22
Final answer:
The equation of the line: y= 5x -22