Question

The line contains the point (9,-9) and has the same y-intercept as y + 1 = 4 (x - 2). Write the equation of this line in slope-intercept form.

Answer 1

The equation for this line, in slope-intercept form, is given by:

`y = - 9`

Explanation:

The equation of a line in the slope-intercept form has the following format:

`y = ax + b`

In which a is the slope of the line and b is the y intercept.

Solution:

The line has the same y-intercept as
`y + 1 = 4 (x - 2)`.

So, we have to find the y-intercept of this equation

`y + 1 = 4 (x - 2)`

`y = 4x - 8 - 1`

`y = 4x - 9`

This equation, has the y-intercept = -9. Since this line has the same intercept, we have that
`b=-9`.

Fow now, the equation of this line is

`y = ax - 9`

The line contains the point
`(9,-9)`

This means that when
`x = 9, y = -9`. We replace this in the equation and find a

`y = ax - 9`

`-9 = 9a - 9`

`9a = 0`

`a = (0)/(9)`

`a = 0`

The equation for this line, in slope-intercept form, is given by:

`y = - 9`