SOLUTION: a) Perpendicular lines have the SAME slope. (TRUE/FALSE) b) The equation of the line that goes through points (3,-9) and (-2,-4) is y = -x

SOLUTION: a) Perpendicular lines have the SAME slope. (TRUE/FALSE) b) The equation of the line that goes through points (3,-9) and (-2,-4) is y = -x - 6. (TRUE/FALSE)

Question 1169616: a) Perpendicular lines have the SAME slope. (TRUE/FALSE)
b) The equation of the line that goes through points (3,-9) and (-2,-4) is y = -x - 6. (TRUE/FALSE)

Found 2 solutions by math_helper, Theo:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
a) FALSE. Perpendicular lines have slopes that are related by
b) y-y0 = m(x-x0), m = (-4-(-9)) / (-2-3) = 5/(-5) = -1
y-(-9) = -1*(x - 3)
y+9 = -x+3
subtract 9 from both sides:
y = -x-6 (TRUE)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the slope of a line perpendicular to the slope of another line is the negative reciprocal of the slope of the other line.

therefore, perpendicular lines do not have the same slope.

your selection a is false.

parallel lines do, however, if they have a different y-intercept.

if they have the same slope and the same y-intercept they are identical.

the equation of the line going through the points (3,-9) and (-2,-4) is determined as follows:

the slope intercept form of the equation of a straight line is y = mx + b

m is the slope
b is the y-intercept.

assign (3,-9) to (x1,y1)
assign (-2,-4) to (x2,y2)

equation for the slope is (y2-y1)/(x2-x1).
that becomes (-4--9)/-2-3) which becomes 5/-5 which becomes -1.
the equation becomes y = -1*x + b
solve for b by replacing x and y with the value of one of the points and then solving for b.
i chose (-2,-4)
the equation becomes -4 = -1 * -2 + b
simplify to get -4 = 2 + b
solve for b to get b = -6
the equation becomes y = -x - 6

your selection b is true.

here's the graph of the equation.

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