Question

Write an equation that represents the line.
Use exact numbers.

Answer 1

`\displaystyle\\Answer:\ (7)/(5)x +(34)/(5)`

Explanation:

`\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\(x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1) \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\(x-(-7))/(-2-(-7)) =(y-(-3))/(4-(-3))\\\\(x+7)/(-2+7)=(y+3)/(4+3) \\\\(x+7)/(5) =(y+3)/(7) \\\\`

Multiply both parts of the equation by 7:

`\displaystyle\\7((x+7)/(5) )=y+3\\\\7((1)/(5) x+(7)/(5) )=y+3\\\\(7)/(5)x +(49)/(5) =y+3\\\\(7)/(5)x +(49)/(5) -3=y+3-3\\\\(7)/(5)x +(49)/(5)-3=y\\\\(7)/(5)x +(49-3(5))/(5) =y\\\\(7)/(5)x +(49-15)/(5) =y\\\\(7)/(5)x +(34)/(5) =y\\\\So,\ y=(7)/(5)x +(34)/(5)`