Question

Write an equation of the line that passes through the given points:

there are four questions:

   1) (0,-1);(6,8)
   2) (3,1);(9,7)
   3) (1,2);(10,14)
   4) (0,0);(-3,5)

Answer 1

y=ax+b
1) we put this points into general formula

`\left \{ {{-1=a*0+b} \atop {8=6a+b}} \right.\\b=-1\\8=6a-1\\6a=9\\a= (3)/(2)`

`y= (3)/(2)x-1`
2)

`\left \{ {{1=3a+b} \atop {7=9a+b}} \right. \\ b=1-3a\\7=9a+1-3a\\6a=6\\a=1\\b=1-3*1=-2\\y=x-2`
3)

`\left \{ {{2=a+b} \atop {14=10a+b}} \right.\\b=2-a\\14=10a+2-a\\12=9a\\a= (4)/(3) \\b=2- (4)/(3)=(2)/(3)\\y=(4)/(3)a+(2)/(3)`
4)

`\left \{ {{0=b} \atop {5=-3a+b}} \right.\\5=-3a\\a=- (5)/(3)\\y=-(5)/(3)a`