How do I the linear function of f (x) with slope -2 such that f (-4)=23?

2 Answers

Hence it is linear it should have the form #f(x)=a*x+b#
where #a=-2# and #f(-4)=23=>8+b=23=>b=15#

Hence it is #f(x)=-2x+15#

Mar 24, 2018

#f(x) = -2x+15#

Explanation:

Start with the slope-intercept form of the equation for a linear function:
#f(x) = mx+b#

Substitute #-2# for #m# (which represents the slope), #-4# for #x#, and #23# for #f(x)#:
#(23) = (-2)(-4) + b#

Then simplify and solve for b by subtracting #8# from both sides:
#23 = 8 + b#
#15 = b#

Finally, substitute #-2# for #m# and #15# for #b# into the slope-intercept form of the equation for a linear function:
#f(x) = (-2)x+(15)#
#f(x) = -2x+15#