How do you graph #2x+5y=10# using intercepts?

2 Answers
Mar 19, 2017

Answer:

Graph of #y=-2/5x+2#
graph{-2/5x + 2 [-7, 7, -7, 7]}

Explanation:

The equation of a straight line with gradient #m# and #y#-intercept #c# is:

#y=mx+c#

You have been given all the information you need but to get to this format, need to rearrange:

#2x+5y=10#

subtracting #2x# from each side gives

#-2x+2x+5y=10-2x#

#5y=-2x+10#

Dividing through both sides by #5# gives

#(5y)/5=(-2x)/5+10/5#

#y=-2/5x+2#

So now it can be seen that the #y#-intercept is #2# and the gradient is #-2/5#.

The #x#-intercept can be found when #y=0#:

#0=-2/5x+2#

To find the value of #x# this again needs rearranging:

#0+2/5x=-2/5x+2+2/5x#

#2/5x=2#

#2/5x xx5/2=2xx5/2#

#x=10/2=5#

So the #x#-intercept is at #5#.

This means that the graph will cross through:

the #x#-intercept #(0,5)#; and

the #y#-intercept #(2,0)#.

You can mark these on your graph and then draw a line through them both.

Graph of #y=-2/5x+2#
graph{-2/5x + 2 [-7, 7, -7, 7]}

Mar 19, 2017

Answer:

see explanation.

Explanation:

To find the intercepts.

#• " let x = 0, in the equation, for y-intercept"#

#• " let y = 0, in the equation, for x-intercept"#

#x=0to0+5y=10toy=2larrcolor(red)" y-intercept"#

#y=0to2x+0=10tox=5larrcolor(red)" x-intercept"#

Plot the points (0 ,2) , (5 ,0) and draw a straight line through them. This is the graph of 2x + 5y = 10
graph{-2/5x+2 [-10, 10, -5, 5]}