[tex]\displaystyle\\Answer:\ y=\frac{8}{3}x-5[/tex]
Step-by-step explanation:
(0,-5) (3,3)
Equation of a straight line:
[tex]\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1} \\\\x_1=0\ \ \ \ x_2=3\ \ \ \ y_1=-5\ \ \ \ y_2=3\\\\Hence,\\\\\frac{x-0}{3-0} =\frac{y-(-5)}{3-(-5)}\\\\\frac{x}{3} =\frac{y+5}{3+5} \\\\\frac{x}{3} =\frac{y+5}{8} \\[/tex]
Multiply both parts of the equation by 24:
[tex](8)(x)=(3)(y+5)\\8x=(3)(y)+(3)(5)\\8x=3y+15\\8x-15=3y+15-15\\8x-15=3y[/tex]
Divide both parts of the equation by 3:
[tex]\displaystyle\\\frac{8}{3}x-5=y[/tex]
