SOLUTION: Consider the line 2x-5y= −1 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Algebra ->  Equations -> SOLUTION: Consider the line 2x-5y= −1 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?      Log On


   

Question 997501: Consider the line
2x-5y= −1
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
to answer these questions, convert the eqation of the line to y = mx + b format.
m is the slope
b is the y-intercept.

the equation is 2x - 5y = -1
subtract 2x from both sides of this equation to get -5y = -2x - 1
divide both sides of this equation by -5 to get:
y = -2/-5 * x - 1/-5
simplify to get:
y = 2/5 * x - (-1/5)
simplify further to get:
y = 2/5 * x + 1/5
the slope is 2/5.
a line that is parallel to this line will have the same slope and a different y-intercept.
a line that is perpendicular to this line will have a slope that is a negative reciprocal of this line.
that line will have a slope of -5/2.

the following graph shows you the relationship between three lines.
the first line is y = 2/5 * x - 1/5
the second line is y = -2/5 * x - 1/5
the third line is y = -2/5 * x + 1/5

the second and third lines are both perpendicular to the first line because their slopes are negative reciprocals of the slope of the first line.

the second line will intersect with the first line on the y-axis because their y-intercepts are the same.

the third line will intersect with the first line at a different point because their y-intercepts are different.

the second line will be parallel to the third line because they are both perpendicular to the same line.

shown below is the graph of the 3 lines.

the red line is the first line.
the blue line is the second line.
the green line is the third line.

the y-intercepts of each line is shown.

the blue line and the red line have the same y-intercept.
that is why they intersect at the y-intercept of each line.

the green line has a different y-intercept.
that is why it intersects with the red line at a different point on the graph.

the blue line will never intersect with the green line because they are parallel to each other (they have the same slope).

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