Question

Find the equation (in terms of xx ) of the line through the points (-4,1) and (3,-2)

Answer 1

First, find the slope of the line that passes through the given points using the slope formula:

`m=(\Delta y)/(\Delta x)`

Next, substitute the value of the slope and the coordinates of one of the given points into the slope-intercept form of the equation of a line to find the y-intercept b:

`y=mx+b`

Compute the value of the slope:

`\begin{gathered} m=((-2)-(1))/((3)-(-4)) \\ =(-2-1)/(3+4) \\ =(-3)/(7) \\ =-(3)/(7) \end{gathered}`

Replace m=-3/7, x=-4 and y=1 into the slope-intercept form of the equation of a line:

`\begin{gathered} \Rightarrow1=-(3)/(7)(-4)+b \\ \Rightarrow1=(12)/(7)+b \\ \Rightarrow1-(12)/(7)=b \\ \Rightarrow-(5)/(7)=b \\ \therefore b=-(5)/(7) \end{gathered}`

Replace m=-3/7 and b=-5/7 to get the equation of the line through the points (-4,1) and (3,-2):

`y=-(3)/(7)x-(5)/(7)`

Therefore, the answer is:

`y=-(3)/(7)x-(5)/(7)`