How do you graph #4x - 3y = 6#?

2 Answers
Aug 18, 2017

Answer:

Find the intercepts with the two axes and draw a line through it.

Explanation:

Given:

#4x-3y=6#

Since this equation contains just linear or constant terms, it describes a straight line.

If we put #x=0# or equivalently cover up the term #4x#, then we get:

#-3y=6#

Dividing both sides by #-3#, this becomes:

#y = -2#

So the line passes through #(0, -2)#

If we put #y=0# or equivalently cover up the term #-3y#, then we get:

#4x=6#

Dividing both sides by #4#, this becomes:

#x = 6/4=3/2#

So the line passes through #(3/2, 0)#

Now we can draw our line through these two intercepts:

graph{(4x-3y-6)(x^2+(y+2)^2-0.005)((x-3/2)^2+y^2-0.005)=0 [-5.17, 4.83, -3.42, 1.58]}

Aug 18, 2017

Answer:

Refer to the explanation for the process.

Explanation:

Graph:

#4x-3y=6# is the standard form for a linear equation.

We can graph it by solving for the x-intercept #(x,0)# and y-intercept #(0,y)#. We only need two points to plot a straight line from a linear equation.

X-Intercept

Set #y=0# and solve for #x#.

#4x-3(0)=6#

#4x=6#

Divide both sides by #4#.

#x=6/4#

Simplify.

#x=3/2#

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

Y-Intercept

Set #x=0# and solve for #y#.

#4(0)-3y=6#

#-3y=6#

Divide both sides by #-3#.

#y=-6/3#

Simplify.

#y=-2#

y-intercept: #(0,-2)#

Plot the x- and y-intercepts on a grid and draw a straight line between the points.

graph{4x-3y=6 [-10, 10, -5, 5]}