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What is the slope-intercept form of the linear equation 2x + 3y = 6?Drag and drop the appropriate number, symbol, or variable to each box.33-61yX1CONmla12/3236+=

What Is The Slopeintercept Form Of The Linear Equation 2x 3y 6Drag And Drop The Appropriate Number Symbol Or Variable To Each Box3361yX1CONmla123236 class=

Sagot :

A line equation can be written in slope-intercept form, which is

[tex]y=mx+b[/tex]

where m represents the slope and b represents the y-intercept.

The line equation on our problem is written in standard form. The given line equation is

[tex]2x+3y=6[/tex]

To rewrite in slope intercept form, let's start by subtracting 2x from both sides:

[tex]\begin{gathered} 2x+3y-2x=6-2x \\ 3y=-2x+6 \end{gathered}[/tex]

Then, let's multiply both sides by 1/3:

[tex]\begin{gathered} \frac{1}{3}\cdot3y=\frac{1}{3}\cdot(-2x+6) \\ y=-\frac{2}{3}x+2 \end{gathered}[/tex]

Thus, this is our equation written in slope-intercept form

[tex]y=-\frac{2}{3}x+2[/tex]

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