How do you find the slope and intercept of #2x+3y=6#?

2 Answers
Jul 19, 2018

Answer:

Slope: #-2/3#
x-intercept: #(3, 0)#
y-intercept: #(0, 2)#

Explanation:

#2x + 3y = 6#

To find the slope, first make the equation into slope-intercept form:
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Subtract #color(blue)(2x)# from both sides of the equation:
#2x + 3y quadcolor(blue)(-quad2x) = 6 quadcolor(blue)(-quad2x)#

#3y = 6 - 2x#

Divide both sides by #color(blue)3#:
#(3y)/color(blue)3 = (6-2x)/color(blue)3#

#y = 2 - 2/3x#

We know that the slope is the value multiplied by #x#, meaning that the slope is #-2/3#.

#--------------------#

To find the x-intercept, plug in #0# for #y# and solve for #x#:
#0 = 2 - 2/3x#

Simplify:
#-2 = -2/3x#

#3 = x#

So the #x#-intercept is at #(3, 0)#.

#---------------------#

To find the y-intercept, plug in #0# for #x# and solve for #y#:
#y = 2 - 2/3(0)#

#y = 2 - 0#

#y = 2#

So the #y#-intercept is at #(0, 2)#.

Hope this helps!

Jul 19, 2018

Answer:

See below:

Explanation:

We can find the #x#-intercept by setting #y# equal to zero. We get

#2x=6=>x=3#

This is our #x#-intercept.

Similarly, we can set #x# equal to zero to find the #y#-intercept. We get

#3y=6=>y=2#

This is our #y#-intercept.

Next, we can convert this equation into slope-intercept form

#y=mx+b#, with slope #m#

We can start by subtracting #2x# from both sides to get

#3y=-2x+6#

Next, divide both sides by #3# to get

#y=-2/3x+2#

We see that our slope, the coefficient on #x# is #-2/3#.

Hope this helps!