Question

The slope of the line below is 1.write the point-slope equation for the line using the coordinates of the labeled point.

Answer 1

`y-4=(x-11)` or
`y=(x-11)+4`

Explanation:

We know that the slope of the line is 1, so we can write it in terms of any two points belonging to the line, as per the difinition of slope:

`slope=(y_1-y_0)/(x_1-x_0) \\1=(y_1-y_0)/(x_1-x_0)`

We can use instead of
`(x_1,y_1)` any general point (x,y) on the line, and for
`(x_0,y_0)` the point we are interested in: (11,4)

That way the slope can be written as:

`1=(y-4)/(x-11)`

Next we can solve for y if this format is the one your instructor prefers:

`1=(y-4)/(x-11)\\1(x-11)=(y-4)\\(x-11)+4 =y`