Question

How do you write the equation of a line in slope-intercept form that passes through (4, 1) and (1,-2)?

Answer 1

`y=x-3`

Explanation:

Begin by finding the slope of the two points by using the slope formula: `m=(y_2-y_1)/(x_2-x_1)`

If we let `(4,1)->(color(blue)(x_1),color(red)(y_1))` and `(1,-2)->(color(blue)(x_2),color(red)(y_2))` Then,

`m=color(red)(-2-1)/(color(blue)(1-4))=-3/-3=1`

Now that we have our slope of `1` we must find our y-intercept or `b` if we are using `y=mx+b` form by substituting our slope `m` and any of the two points given and solving for b.

`1=1(4)+b`

`1=4+b`

`1-4=cancel(4-4)+b`

`-3=b`

So our final equation is `y=1x-3` or simply `y=x-3`