Question

How do you write the equation of the line with (0,-1) (3,-5)?

Answer 1

`color(blue)(y=-3/4 x -11/4)`

Explanation:

You can use the two point to provide the gradient of the line. Then by substitution of one of these points determine the value of the constant.

standard equation form `->y=mx+c`

Where `m` is the gradient and `c` is the constant of the y intercept

Let Point 1 be `P_1->(x_1,y_1) -> (0,-1)`
Let point 2 be `P_2->(x_2,y_2)->(3,-5)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the gradient")`

gradient (m) is `" "("change in y")/("change in x")`

`=> m=(y_2-y_1)/(x_2-x_1) -> (3-0)/(-5-(-1))`

`color(blue)(=> m= 3/-4 = -3/4)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Determine the constant c")`

At `P_2 ->y=(-3/4)x+c" "-> -5=(-3/4)(3)+c`

`color(blue)(=> c=-5+9/4 = -2 3/4 =-11/4)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`color(blue)(y=-3/4 x -11/4)`