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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+-%281%2F2%29x-4
a) Substitute -4 for every instance of x and simplify.
f%28x%29=+-%281%2F2%29x-4
f%28-4%29=+-%281%2F2%29%28-4%29-4
f%28-4%29=+2-4
highlight_green%28+f%28-4%29=+-2%29
.
.
b)To find the x-intercept, set f(x)=y=0 and solve for x.
f%28x%29=+-%281%2F2%29x-4
+-%281%2F2%29x-4=0
+-%281%2F2%29x=4
highlight_green%28+x=-8%29
(-8,0)
.
.
c)To find the y-intercept, set x=0 and solve for f(x) or y.
f%28x%29=+-%281%2F2%29x-4
f%28x%29=+-%281%2F2%29%280%29-4
highlight_green%28+f%28x%29=+-4%29
(0,-4)
.
.
d)The line is in slope-intercept form, y=mx%2Bb, where m is the slope.
highlight_green%28+m=-1%2F2%29
.
.
e)Perpendicular lines have slopes that are negative reciprocals of each other.
m1%2Am2=-1
-%281%2F2%29%2Am2=-1
m2=2
A line perpendicular to the given line will have a slope of highlight_green%28+m=2%29.
.
.
Here's a graph of the original line and a perpendicular line y=2x.
.
.

.
.
The given line is in red (Note the x and y intercepts)
The perpendicular line is in green.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+-1%2F2x-4
a) find f(-4)
Plug in -4 fox x and solve
f%28-4%29=+%28-1%2F2%29%2A4-4
f%28-4%29=+-2-4
f%28-4%29+=+-6
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
f%28x%29=+%28-1%2F2%29x-4
0+=+%28-1%2F2%29x+-+4
4+=++%28-1%2F2%29x
-8+=+x
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
f%28x%29=+%28-1%2F2%29x-4
f%28x%29=+%28-1%2F2%29%2A0-4
f%28x%29=+-4
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