l is given find the slope of a line that is a)parallel to l and b)perpendicular
ID: 3102881 • Letter: L
Question
l is given find the slope of a line that is a)parallel to l and b)perpendicular to ly=8
find an equation for the line with the given prperties. express using either general form or slope-intercept form of the equationof a line
parralel to the line y=-3x; containing the point -1,2
perpendicular to the line y=2x-3; containing point 1,-2
the eauations of 2 lines are given detemine if they are parallel, perpendicular or neither
y=-2x+3; y=-1/2x+2
use slopes to show that the quadrilateral whose vertices are (1,-1), (4,1),(2,2) and (5,4) is a parralelagram
find an equation of the line containing the centers of 2 circles
x^2 +y^2-4x+6y+4=0 and x^2+y^2+6x+4y+9=0
Explanation / Answer
Question 1 Since the line y=8 is a horizontal line (that crosses the y-axis at 8), its slope is 0. a)A line parallel to y=8 would have the same slope. b)A line perpendicular to y=8 would have a slope equal to the opposite reciprocal of the slope of the line y=8. Remember that if there is a zero in the denominator of a fraction, the value of the fraction is undefined. Question 2 Since the line whose equation we are looking for is parallel to the line y=-3x, it will have the same slope as this line. Remember slope is the value of m if the equation is in slope intercept form (y=mx+b). Since the line whose equation we are looking for passes through the point (-1,2), we can substitute this x and y value, and the slope of the line, into the form y=mx+b, and then solve that equation for b. Once we have the b value, then we will substitute only the values m and b into the form y=mx+b to get the equation for the line. Question 3 Remember that the slope of a line is the m value if the equation of the line is in slope-intercept form, y=mx+b. If the slopes of the two lines are equal, then the lines are parallel. If the slopes are opposite reciprocals, then the lines are perpendicular. If the slopes are neither equal nor opposite reciprocals, then the lines are neither parallel nor perpendicular. The only exception to that of course is if one line has a slope of zero and the other line's slope is undefined, then the lines are perpendicular. Question 4 Change each circle's equation into standard form by using completing the square technique: x^2+y^2-4x+6y+4=0 x^2-4x+4 + y^2+6y+9 = 9 (x-2)^2 + (y+3)^2 = 9 So the center of this circle is at (2,-3). Change the other equation into standard form and determine the circle's center. Next, find the slope of the line passing through the two centers using slope formula. Then substitute the slope and one of the center's coordinates into the form y=mx+b, and solve for b. Then substitute only the m and b values into y=mx+b to get the equation asked for.
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