SOLUTION: ----------- --- QUESTION FOLLOWS ----------- ----------- -- Given the linear function f(x)= -1/2x-4: a) find f(-4) b) Determine the coordinates of the x-intercept c) Determin

Question 312742: --------------- QUESTION FOLLOWS --------------------------
Given the linear function f(x)= -1/2x-4:
a) find f(-4)
b) Determine the coordinates of the x-intercept
c) Determine the coordinates of the y-intercept
d) Determine the slope
e) Determine the slope of a line perpendicular to this line.
*** Can you explain your answers to help me understand better?
Found 2 solutions by Fombitz, vleith:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

a) Substitute -4 for every instance of x and simplify.

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b)To find the x-intercept, set f(x)=y=0 and solve for x.

(-8,0)
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c)To find the y-intercept, set x=0 and solve for f(x) or y.

(0,-4)
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d)The line is in slope-intercept form, , where m is the slope.

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e)Perpendicular lines have slopes that are negative reciprocals of each other.

A line perpendicular to the given line will have a slope of .
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Here's a graph of the original line and a perpendicular line .
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.

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The given line is in red (Note the x and y intercepts)
The perpendicular line is in green.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!

a) find f(-4)
Plug in -4 fox x and solve

b) Determine the coordinates of the x-intercept
x intercept is found when the y coordinate is 0. So set f(x) = 0 and solve

x intercept is (-8,0)
c) Determine the coordinates of the y-intercept
y intercept is found when x coordinate equal 0. Set x=0 and solve

y intercept is the point (0, -4)
d) Determine the slope
use slope intercept form of a line. This equation is already in that form (y = mx +b).
So the slope is -1/2
e) Determine the slope of a line perpendicular to this line.
Perpendicular lines have slopes that are negative reciprocals of each other
so when their slopes are multiplied together, the result is -1
Slope for perp line is therefore -1/(-1/2) = 2
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