Question

How do you write an equation in standard form for a line which passes through points (-10,3) and (-2,-5)?

Answer 1

The equation of the line is `y = -x-7`.

To find this, note that we are looking for an equation of the form:

`y = mx+c`

for some constant slope `m` and intercept `c`.

The slope `m` can be calculated as:

`m = (Delta y)/(Delta x) = (-5-3)/(-2-(-10)) = (-8)/8 = -1`

where `Delta y` means the change in `y` and `Delta x` means the change in `x`.

So we now know that `y = mx+c = (-1)x+c = -x+c`.

Add `x` to both ends to get `y+x=c`. Subsitute in either of our points to calculate `c`. Let us use `x=-10` and `y=3`:

`c=y+x=3+(-10)=3-10=-7`.

So `m = -1` and `c = -7`, giving `y=-x-7`.