You must learn some facts about lines, their graphs
and their equations.
(1). The equation of a non-vertical graphed line that goes through point
(x1,y1) and has slope is
(2).
(3). The equation of a non-vertical graphed line that has slope and
y-intercept is
(4). Two non-vertical parallel lines have the same slope.
(5). Two non-vertical perpendicular lines have slopes one of which
is the reciprocal of the other with the sign changed.
(6). A vertical line has no slope and has the equation where
represents its distance from the y-axis, right of the y-axis
if is positive and left of the y-axis if is negative.
is the equation of the vertical line that coincides with
the y-axis.
(7). A horizontal line has slope .
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write an equation for each line, then graph the line.
through (-1,3) and parallel to
We draw the line by plotting a couple of points
and draw it in light green:
Next we plot the point (-1,3)
And we draw a black line through that point
parallel to the green line:
That black line is the line we need the equation for.
So, from we use (3) above to find that
From (4) we know that we will use the same slope .
Next we use (1) to find the equation:
where (x1,y1) = (-1,3)
and
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through (2,2) and perpendicular to
We draw the line by plotting a couple of points
and draw it in light green:
Next we plot the point (2,2)
And we draw a black line through that point
perpendicular to the green line:
That black line is the line we need the equation for.
So, from we use (3) above to find that
From (5) we know that we will use the slope which is found
by inverting and changing its sign, and so we
use for the black line.
Next we use (1) to find the equation:
where (x1,y1) = (2,2)
and
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through (-3,4) and vertical
We plot the point:
and draw a vertical line through it:
Now we use (6) above and realize that the vertical line is 3
units to the left of the the y-axis and thuse its equation
is
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through (4,1) and horizontal
We plot the point:
and draw a horizontal line through it:
Now we use (7) above which tells us the slope
Next we use (1) to find the equation:
where (x1,y1) = (4,1)
and
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Edwin