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Posted by dolphin@eskimo.com (64.24.214.84) on August 18, 2001 at 17:18:17:
In Reply to: Help me solve this equation. posted by on August 18, 2001 at 15:28:55:
There are a couple of things to know before starting this problem.
1) The point-slope formula is used to find the equation of a line when you know the line's slope and one point on the line.
2) The slopes of perpendicular lines are negative recipricals of each other.
We are told that the line is perpendicular to the line y = 2x - 4. Well, this equation is in slope-intercept form (y = mx + b), so we can read off the slope by inspection. Its slope is 2. The negative reciprical of 2 is -1/2.
Now we know both the slope of our line (-1/2) and one point on our line (-1,4).
The point-slope formula can now be used to find the equation of our line:
y - y1 = m(x - x1) where m is the slope and (x1,y1) is the point.
y - 4 = -(1/2)(x + 1)
y - 4 = -(1/2)x - 1/2
y = -(1/2)x + 7/2
This is the equation of the line that passes through (-1,4) and is perpendicular to y = 2x - 4.
To find the point of intersection, we need to realize that the coordinates of this point must satisfy both equations:
y = 2x - 4
y = -(1/2)x + 7/2
Since y = y, these expressions for y must be equal.
2x - 4 = -(1/2)x + 7/2
(5/2)x = 15/2
x = 3
Now that we know the x-coordinate of the intersection point, we can find the y-coordinate by substituting this value for x in either equation.
y = 2x - 4
y = 2(3) - 4
y = 2
The intersection point is (3,2)
~ Mark