Write the equation of the line fully simplified slope-intercept form.​

Answer: The equation of the line fully simplified slope-intercept form:[tex]y\:=\:\frac{5}{3}x-5[/tex]Step-by-step explanation:We know the slope-intercept form of the line equation is[tex]y = mx + b[/tex]where m is the slope and b is the y-interceptGiven the points on the line(0, -5)(3, 0)Finding the slope between the points (0, -5) and (3, 0)[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\left(x_1,\:y_1\right)=\left(0,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:0\right)[/tex][tex]m=\frac{0-\left(-5\right)}{3-0}[/tex][tex]m=\frac{5}{3}[/tex]We know the y-intercept can be determined by setting x = 0 and solving for y.From the graph, it is clear thatat x = 0, y = -5Thus, the y-intercept = b = -5now substituting b = -5 and m = 5/3 in the slope-intercept form[tex]y = mx+b[/tex][tex]y\:=\:\frac{5}{3}x+\left(-5\right)[/tex][tex]y\:=\:\frac{5}{3}x-5[/tex]Thus, the equation of the line fully simplified slope-intercept form:[tex]y\:=\:\frac{5}{3}x-5[/tex]