The equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]
Further explanation:
The standard slope-intercept form is:
[tex]y=mx+b[/tex]
Given equation is:
[tex]-2x+3y=6[/tex]
In order to bring the equation in slope-intercept form we have to isolate y on left hand side of equation
So,
Adding 2x on both sides
[tex]-2x+3y+2x=6+2x\\3y=2x+6[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{2x+6}{3}\\y=\frac{2x+6}{3}[/tex]
Simplifying
[tex]y=\frac{2x+6}{3}\\y = \frac{2x}{3}+\frac{6}{3}\\y=\frac{2}{3}x+2[/tex]
The equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]
Keywords: Slope-intercept form, linear equation
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