How do you find the slope and y intercept for #y = -2x + 7#?

1 Answer
Jan 3, 2016

Answer:

#color(purple)("Look at the very detailed method used/explained in my solution.")#

Explanation:

Tony B

#color(blue)("Slope or gradient")#
The slope is the amount of up or down for the amount of along and is directly related to the change in #x# and the change in #y#.
So if you had say, 6 down (change in y value) for 3 along (change in x value) the slope is #color(white)(..)(6 " up or down")/(3 " along")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
But if we treat this as a ratio and divide both numerator and denominator by 3 we have:

#( 6 -: 3)/(3 -: 3) = 2/1 = 2 #

So for every 1 along we have 2 up or down.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We need to have a way of showing if the slop is upwards or downwards. The convention for this is that if we have -2 then the slope is downwards if we move from left to right. In which case +2 means upwards.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("So your question has a downward slop of " -2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("x intercept")#
This is when the line crosses the x-axis. The x-axis it at #y=0#
So to find this we substitute #y=0 " into " y=-2x+7# giving:

#0=-2x+7#
Add #2x# to both sides giving:
#0+2x=2x-2x+7#
#2x=0+7#
Divide both sides by 2 giving:
#2/2 x=7/2#
#1 xx x =7/2 = 3 1/2#
#color(brown)(x_("intercept")= 3 1/2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("y intercept")#

This when the line crosses the y-axis. The y-axis is at #x=0#. So we substitute #x=0# into #y=-2x+7# giving

#y = (2 xx 0) + 7#

#color(brown)(y_("intercept")= 7#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~