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

2 Answers
Apr 10, 2018

Answer:

By converting it into slope-intercept form and then inputting x's to get y's.

Explanation:

The easiest way to solve this is to convert it into slope-intercept form, which is #y=mx+b#.

You subtract #-4x# on both sides to get

#-3y=-4x-6#.

Then you divide #-3# on both sides to isolate y, and you are left with

#y=4//3x-2#.

Then, you would input x-inputs to get y-inputs for your points.

So if your x-input is 2, then you would do this

#y=4//3(2)-2# or just #y=2//3#.

Apr 10, 2018

Answer:

Please read the explanation.

Explanation:

#" "#
Given:

The Linear Equation: #color(red)(4x-3y=6#

Note that this is the equation of a straight line.

The most common form of the equation is #color(blue)(y=mx+b#, where

#color(blue)(m# is the Slope or the Gradient, and

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

This form is referred to as the Slope-Intercept Form.

#color(green)("Step 1"#

Reduce #color(red)(4x-3y=6# to the Slope-Intercept Form.

#4x-3y=6#

Get #color(blue)(y# on one side of the equation and the rest on the other side.

Subtract #4x# from both sides.

#rArr 4x-3y - 4x=6-4x#

#rArr cancel (4x)-3y - cancel(4x)=6-4x#

Rearrange the terms as

#rArr -3y = -4x+6#

Rewrite pulling #(-1)# out from both sides:

#rArr -1(3y) = -1(4x-6)#

Divide both sides by #(-1)# to simplify.

#rArr ((-1)(3y))/(-1) = ((-1)(4x-6))/(-1)#

#rArr (cancel(-1)(3y))/cancel(-1) = (cancel(-1)(4x-6))/cancel(-1)#

#rArr 3y=4x-6#

Keep #color(blue)(y# on the left-hand side and move #color(blue)(3# to the right-hand side of the equation.

Divide both the sides of the equation by #color(blue)3#.

#rArr (1/3)(3y)=(1/3)(4x-6)#

#rArr (1/cancel 3)(cancel 3y)=(1/3)(4x-6)#

Distribute #(1/3)# into the expression.

#rArr y = (1/3)(4x)-(1/3)(6)#

#rArr y = (1/3)(4x)-(1/cancel 3)(cancel 6^color(red)2))#

#rArr y = (4/3)x-2#

Observe that #color(blue)(y = (4/3)x-2# is in the Slope-Intercept Form.

where

#color(blue)(m=(4/3)# is the Slope or the Gradient, and

#color(blue)(b=(-2)# is the y-intercept.

For this equation generate a table with #x# and #y# values:

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Using this table of values, create a graph as shown below:

enter image source here

Hope it helps.