Question

What is the equation of this line in standard form? −6x+11y=13 −6x+7y=−17 −6x+11y=−13 −11x+6y=−13 Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points begin ordered pair negative four comma negative one end ordered pair and begin ordered pair one and begin fraction one-half end fraction comma, two end ordered pair

Answer 1

What is the equation of this line in standard form?

6x−11y=−13

is the answer

Answer 2

Given that the line passes through the points
`(-4,\ -1)` and
`(1 (1)/(2), \ 2)`

The equation of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by:


`(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)`

Thus, the required equation is obtained as follows:


`(y-(-1))/(x-(-4)) = (2-(-1))/(( (3)/(2)) -(-4)) \\ \\ \Rightarrow (y+1)/(x+4) = (2+1)/( (3)/(2)+4)= (3)/( (11)/(2) )= (6)/(11) \\ \\ \Rightarrow 11(y+1)=6(x+4)\\ \\ \Rightarrow 11y+11=6x+24\\ \\ \Rightarrow \bold{-6x+11y=13}`