Slope 2/3; y-intercept (0, -2)
3x + 5y = 10
*Inverse of mult. by 5 is div. by 5
*Slope/intercept form of the line
I got m = -3/5 and y-intercept
is 2.
Passes through (-3, 2) and has a slope of -1/2.
Looks like we have all the information we need. We are ready to
put our equation together. Since we don't have the y-intercept, we
will have to use the point/slope form since that is set up for ANY point (not just the y-int.).
*Inverse of sub. 2 is add 2
*LCD is 2
*Mult. 2/1 by 2/2 to get 4/2
*Slope/intercept form of the line
(0, 0) and (5, 10)
We have more than enough points. However, what about the slope? Does this mean we can't work out the problem? You are not going to get off that easily. We do have a way of finding the slope. Tutorial 15: The Slope of a Line shows us how we can get the slope given two points.
Let's find that slope:
*Plug in values
*Simplify
Slope 0; passes through (1, 2)
Since it passes through (1, 2), and a horizontal line is in the form y = c, where the y value is ALWAYS equal to the same value throughout, this means our equation would have to be y = 2.
Note that 2 is the y value of the ordered pair given.
Vertical; passes through (-1, -2)
Since it passes through (-1, -2), and a vertical line is in the form x = c, where the x value is ALWAYS equal to the same value throughout, this means our equation would have to be x = -1.
Note that -1 is the x value of the ordered pair given.
Passes through (2, 3) and parallel to 5x + 2y = 4
We have our point. However, what about the slope?
We need to do a little digging to get it.
Recall that Tutorial
15: The Slope of a Line tells us that parallel lines have the same slope.
So, if we know the slope of the line parallel to our line, we have it made.
Find the slope of the parallel line:
*Inverse of mult. by 2 is div. by 2
*Slope/intercept form of the line
OK, now we have our slope, which is -5/2. Now we want to put
the slope and one point into the point/slope equation.
*Inverse of sub. 3 is add 3
*Slope/intercept form of the line
*Function notation
Passes through (-1, 0) and perpendicular to 3x - y = 2
We have our point. However, what about the slope?
We need to do a little work in that department.
Recall that Tutorial
15: The Slope of a Line tells us that the slopes of perpendicular lines
are negative reciprocals of each other. So, if we know
the slope of the line perpendicular to our line, we have it made.
Find the slope of the perpendicular line:
*Slope/intercept form of the line
What did you come up with?
I came up with -1/3 for the slope of our line.
Now we can go on to the equation of our line:
*Slope/intercept form of the line
*Function notation
Last revised on July 5, 2011 by Kim Seward.
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