How do you find the slope given #y + 4x = 5#?

standard form is #y=mx+c, :. y=-4*x+5#
-4 is the slope & 5 the y-intercept.

The standardised equation for a straight line graph is:

#" "y=mx+c#

As #x# can be assigned any value you chose it is called the independent variable

As the value of #y# depends on the value you assign to #x# it is called the dependant variable

The slope (proper name is gradient ) is #m# this represents the amount of up or down for the amount along as you read left to right.
If m is negative then it is a downward slop. If m is positive then it is an upwards slop.

The constant #c# just lifts or lowers the graph. If it is #-c# then the line is lowered by that amount. If it is #+c# then the graph is raised by that amount.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given: #color(brown)(y+4m=5)#

Converting this equation to standard form

Subtract #color(blue)(4m)# from both sides giving:

#" "color(brown)(y+4mcolor(blue)(-4m)" "=" "5color(blue)(-4m))#

#y+0=-4m+5#

#" "color(green)(y=-4x+5)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(magenta)(" So the slope is "-4)#.

This means for 1 along the x-axis y goes down by 4