How do you find the slope and intercept of #x= 2y+2#?

1 Answer
Mar 18, 2016

Answer:

#color(blue)(y_("intercept")=-1)#
#color(blue)(x_("intercept")=2)#
#color(blue)("Gradient "=+2)#

Explanation:

#color(brown)("It does not matter if you have "x=2y+2" or by ")#
#color(brown)("manipulation "y=x/2-1 ". They both plot the same ")##color(brown)("straight line.")#

So the slope #color(blue)("(gradient) is 2")#. That is: for every 1 along you go up 2. You always read from left to right for the gradient.

+2 means the line goes up whilst -2 means it goes down!
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("To determine "x_("intercept"))#

The line will cross the x-axis at y=0

Set y=0 giving:

#x=2(0)+2#

#color(blue)(x_("intercept")=2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine "y_("intercept"))#

The line will cross the y-axis at x=0

Set x=0 giving:

#0=2y+2#

Subtract #color(red)( 2)# from both sides

#0color(red)(-2)=2y+2color(red)(-2)#

#-2=2y+0#

Divide both sides by #color(red)(2)#

#-2/(color(red)(2))=2/(color(red)(2)) xx y#

But #2/(-2)=-1" and "2/2=+1#

#-1=1xxy#

#color(blue)(y_("intercept")=-1)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tony B