Question

What is the equation of the line passing through `(8,2), (5,8)`?

Answer 1

`color(brown)(y= (-2)x+18)`

Explanation:

Assumption: This is for a strait line graph (not stated in question)

Let `(x_1,y_1) -> (8,2)`
Let `(x_2,y_2) -> (5,8)`

Using standard equation for strait line graph.

`y=mx+c`.............(1)

`color(green)("Method: determine gradient(m) Then substitute in equation (1) with")`
`color(green)("known values for x and y to determine the constant's value.")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the gradient")`

gradient `=m =("change in Up or down")/("change in along")`

`color(brown)(m)=(y_2-y_1)/(c_2-x_1)=(8-2)/(5-8) = 6/(-3)= color(brown)(-2)color(white)(...)`.......(2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the value of c")`

Substitute for m and`color(white)(.) (x_1,y_1)` into equation (1)

`2=(-2)(8)+c`

`color(brown)(c= 18)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Bring it all together")`

`color(brown)(y= (-2)x+18)`

`color(green)("Note: as the gradient is negative it is a downward slope")`
`color(green)("as you move from left to right.")`