What is the slope of #y=-x#?

This is in slope-intercept form, or #y = mx + b#, where #m# is the slope and #b# is the #y#-intercept.

Since we know the slope is the value multiplied by #x#, the slope is #-1.#

Hope this helps!

#color(blue)("The concept of slope")#

Slope (gradient) is the amount of up or down on the y-axis for a given amount of along on the x-axis.

Suppose for example the slope is 2.

Another way of writing 2 (which is not done very often) is #2/1#

As slope #->("amount of up or down")/("amount of along")# then we have the amount of 2 as the up or down and we have the value of 1 for along.

As the 2 is positive ,by convention, it is UP.

A negative value for the up or down by convention is DOWN.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Given: #y=-x#

Write this as: #y=-1x larr" bad practice!"#

This is the same as #(-1)/1#

So for 1 along the line goes DOWN 1

Thus the slope is #-1#

Recall slope-intercept form

#y=mx+b#, with slope #m# and a #y#-intercept of #b#. With this in mind, we can rewrite our equation as

#y=-x+0#

We see that our slope, or coefficient on #x#, is #-1#.

Hope this helps!