What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0

Answer:[tex]y = - \frac{ 3}{2} x[/tex]Step-by-step explanation:slope-intercept formy= mx +c, where m is the slope and c is the y-intercept.Let's rewrite the given equation into the slope-intercept form so we can find out its gradient.3x +2y -6= 02y= -3x +6Dividing by 2 throughout:[tex]y = - \frac{3}{2} x + 3[/tex]Thus gradient of given line= [tex] - \frac{3}{2} [/tex]Parallel lines have the same gradient.Thus gradient of line= [tex] - \frac{3}{2} [/tex]Subst. m=[tex] - \frac{3}{2} [/tex] into the equation:[tex]y = - \frac{3}{2}x + c[/tex]To find c, substitute a pair of coordinates.When x=0, y=0,[tex]0 = - \frac{3}{2} (0) + c \\ c = 0[/tex]Thus, the equation of the line is [tex]y = - \frac{3}{2} x[/tex].