Write an equation in slope intercept form that passes through -2, 3 and Is parallel to the line with equation 3X +2y=6

The equation of line is:  [tex]y=-\frac{3}{2}x[/tex] as the y-intercept is zeroStep-by-step explanation:Given(-2,3)Equation of line => 3x+2y=6Converting the equation in slope intercept form[tex]3x+2y=6\\2y=-3x+6\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=-\frac{3}{2}x+\frac{6}{2}\\y=-\frac{3}{2}x+3[/tex]The co-efiicient of x is the slope of the fiven lineSo,m=-3/2The line parallel to given line will have the same slope as slopes of two parallel lines are equalNow,Slope-intercept form is: [tex]y=mx+b[/tex]Putting the value of slope[tex]y=-\frac{3}{2}x+b[/tex]to find the value of b, put (-2,3) in the equation[tex]3=-\frac{3}{2}(-2)+b\\3=3+b\\b=0\\[/tex]Putting the value of b and m[tex]y=-\frac{3}{2}x+0\\y=-\frac{3}{2}x[/tex]Hence,The equation of line is:  [tex]y=-\frac{3}{2}x[/tex] as the y-intercept is zeroKeywords: Slope-intercept form, SlopeLearn more about slope-intercept form at:brainly.com/question/2116906brainly.com/question/2131336#LearnwithBrainly