Question

Write the equation of the line that passes through the given points.

(0,-5) and (3,3)
The equation of the line is
(Simplify your answer. Type your answer in slope-intercept form. Use in

Answer 1

`\displaystyle\\Answer:\ y=(8)/(3)x-5`

Explanation:

(0,-5) (3,3)

Equation of a straight line:

`\displaystyle\\(x-x_1)/(x_2-x_1) =(y-y_1)/(y_2-y_1) \\\\x_1=0\ \ \ \ x_2=3\ \ \ \ y_1=-5\ \ \ \ y_2=3\\\\Hence,\\\\(x-0)/(3-0) =(y-(-5))/(3-(-5))\\\\(x)/(3) =(y+5)/(3+5) \\\\(x)/(3) =(y+5)/(8) \\`

Multiply both parts of the equation by 24:

`(8)(x)=(3)(y+5)\\8x=(3)(y)+(3)(5)\\8x=3y+15\\8x-15=3y+15-15\\8x-15=3y`

Divide both parts of the equation by 3:

`\displaystyle\\(8)/(3)x-5=y`