The equation of the graphed line in point-slope form is?, and it’s equation in slope-intercept form is?

ANSWERPoint-slope form:[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]Slope-intercept form:[tex]y= -\frac{3}{5} x + \frac{9}{5}[/tex]EXPLANATIONThe graphed line passes through[tex](-2,3) \: \: and \: \: (3,0)[/tex]The slope of this line is determined using [tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]We substitute the points to get;[tex]m = \frac{0 - 3}{3 - - 2} [/tex][tex]m = -\frac{3}{5} [/tex]The point-slope formula is:[tex]y-y_1 = m(x - x_1)[/tex]Substitute the first point and slope to get:[tex]y - 3 = -\frac{3}{5} (x - - 2)[/tex][tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]To find the slope-intercept form, we expand to get:[tex]y= -\frac{3}{5} x - \frac{6}{5} + 3[/tex][tex]y= -\frac{3}{5} x + \frac{9}{5} [/tex]