4. (4 pts) Find an equation of the line L which is parallel to the line 2x+3y=5 and which passes through the midpoint of the line segment with endpoints A(-1, 2) and B (5,-8). Simplify your answer to the slope-intercept form. Solution (0, 0.5, 1) The line 2x+3y=5 has slope equal to -2/3 (you tell why). Since L is parallel to the line 2x+3y 5, the slope of L is also -2/3. The coordinates of the midpoint of the line segment joining A and B are: (-1+5 2+(-8)=(2,-3). (0, 0.5, 1) Using the point-slope form, the equation of L is given by: y-(-3)-(x-2) = which simplifies to y - in the slope-intercept form. (0, 1, 2)
4. (4 pts) Find an equation of the line L which is parallel to the line 2x+3y=5 and which passes through the midpoint of the line segment with endpoints A(-1, 2) and B (5,-8). Simplify your answer to the slope-intercept form. Solution (0, 0.5, 1) The line 2x+3y=5 has slope equal to -2/3 (you tell why). Since L is parallel to the line 2x+3y 5, the slope of L is also -2/3. The coordinates of the midpoint of the line segment joining A and B are: (-1+5 2+(-8)=(2,-3). (0, 0.5, 1) Using the point-slope form, the equation of L is given by: y-(-3)-(x-2) = which simplifies to y - in the slope-intercept form. (0, 1, 2)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:4. (4 pts) Find an equation of the line L which is parallel to the line 2x+3y=5 and which passes
through the midpoint of the line segment with endpoints A(-1, 2) and B (5,-8). Simplify your
answer to the slope-intercept form.
Solution
(0, 0.5, 1)
The line 2x+3y=5 has slope equal to -2/3 (you tell why). Since L is parallel to the line
2x+3y 5, the slope of L is also -2/3.
The coordinates of the midpoint of the line segment joining A and
B are:
(-1+5 2+(-8)=(2,-3).
(0, 0.5, 1)
Using the point-slope form, the equation of L is given by:
y-(-3)-(x-2)
=
which simplifies to y
-
in the slope-intercept form.
(0, 1, 2)
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