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 equationSo,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 equationLearn more about slope-intercept form at:brainly.com/question/12954015brainly.com/question/1979240#learnwithBrainly