Question

Determine the equation of a straight line passing through the point (1, 0) and (2, -3)

Answer 1

y = -3x - 3

Explanation:

By equation of a straight line, this could mean:

Slope intercept form:
`y=mx+b`

Point slope form:
`y-y1=m(x-x1)`

Because we do not have the y intercept, it would be much easier to write it in point slope form where y1 and x1 are points and m is the slope.

First, we need to find the slope. We can do this by using the slope formula
`(y2-y1)/(x2-x1)` where y2, y1, x2, and x1 are points.

`(-3-0)/(2-1)`

Evaluate

`(-3)/(1)=-3`

Now that we have the slope, lets use the ordered pair (1,0) and write the equation of the line in point slope form.

`y-0=-3(x-1)`

Simplify

`y=-3x-3`

Would you look at that, we get the equation of the line in slope intercept form!