How do you graph #x-y=1 #?

2 Answers
Jul 29, 2018

Determine the x- and y-intercepts, plot them, and draw a straight line through the point.

Explanation:

Graph:

#x-y=1#

X-intercept: value of #x# when #y=0#

Substitute #0# for #y# and solve for #x#.

x-0=1#

#x=1#

The x-intercept is #(1,0)#. Plot this point.

Y-intercept: value of #y# when #x=0#

Substitute #0# for #x# and solve for #y#.

#0-y=1#

#-y=1#

Multiply both sides by #-1#. This will reverse the signs.

#-1(-y)=1xx-1#

#y=-1#

The y-intercept is #(0,-1)#. Plot this point.

Draw a straight line through the points.

graph{x-y=1 [-10, 10, -5, 5]}

Jul 29, 2018

#" "#
Please read the explanation.

Explanation:

#" "#
We are given the equation: #color(red)(x-y=1#

How do we graph this linear equation ?

We have

#color(blue)(x-y=1#

The given equation can be reduced to a more simpler form.

Subtract #color(red)(x# from both sides of the equation:

#rArr x-y-x=1-x#

#rArr cancel x-y-cancel x=1-x#

#rArr -y = 1-x#

Multiply both sides of the equation by #color(red)((-1)#

#rArr -y*(-1) = (1-x)(-1)#

#rArr y=x-1#

Now, we have the equation in Slope-Intercept Form:

#color(blue)(y=mx+b)#, where

#color(red)(m# is the Slope and

#color(red)(b# is the y-intercept.

Hence,

Slope : #color(blue)(1#

y-intercept :#color(blue)((0,-1)#

The x-intercept is where the graph crosses the x-axis

Set #color(red)(y=0# to find the x-intercept:

#rArr x-1=0#

Add #color(red)(1# to both sides of the equation:

#rArr x-1+1=0+1#

#rArr x-cancel 1+cancel 1=0+1#

#rArr x=1#

Hence #color(red)((1,0)# is the x-intercept.

Plot the points x-intercept and intercept on the graph.

Join the two points to get the straight line.

This is the graph of the linear equation.

enter image source here

Hope you find this solution useful.