Question

How do you write an equation in slope intercept form for the line through the given point (5, -2) and (-16, 4)?

Answer 1

The slope of your line is: `m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)` and represents the inclination of your line (change in `y` for a change in `x`).

In your case you have: `m=(4-(-2))/(-16-5)=6/-21=-2/7`

you can now insert this slope into the relationship:

`y-y_0=m(x-x_0)` that gives the equation of your line using, for example, the coordinates of your first point as:

`y-(-2)=-2/7(x-5)`

giving: `y=(-2/7)x-(4/7)`

So you have a line of slope `m=-2/7` and intercept at `y=-4/7`