How do you find the slope and intercept of #f(x) = -6x - 7#?

1 Answer
Jan 28, 2016

Answer:

#m = -6#
y-intercept #= -7#
x-intercept #= -7/6#

Explanation:

For a linear equation, a way to find the slope and intercept of a function (aside from graphing) is to examine the slope-intercept form of the equation. Generally it looks like this:

#y = mx + b#

Where #m# is the slope and #b# is the y-intercept

In this case, the function you gave is already in the desired format so we do not have manipulate it. If the equation is in another format, we need to do the necessary manipulations (transposing, simplifying etc.) before we can start with the process

The given equation is

#f(x) = -6x - 7#

So comparing it with the general slope-intercept form, we would know that:

  1. The slope is -6 #(m = -6)#
  2. The y-intercept is #-7#

The y-intercept is technically the point at which the graph intersects the y-axis. In this case, another way of getting the value of the y-intercept is by evaluating the equation using #x = 0# (since at the y-axis the value of x is 0. (method seen below)

#f(x) = -6x -7#

when #x = 0#
#y = -6(0) - 7#
#y = -7#

As for the x-intercept, we use the same process done for the y-intercept except we evaluate using #y = 0#. (shown below)

when #y = 0#
#0 = -6x - 7#
#6x = -7#
#x = -7/6#

Final Answer:
#m = -6#
y - intercept #= -7#
x - intercept #= -7/6#