Question

What is the equation of the line with slope `m= -1/4` that passes through `(7,3)`?

Answer 1

The equation of the line would be `y= -1/4x + 19/4`

Explanation:

The formula for the slope intercept form is

`y=mx +b`

where `m` is the slope and `b` is the `y`-intercept. In this problem, you are given the slope or `m`. To find the `y`-intercept, you plug in the point that is given, `(7,3)` into `x` and `y` respectively and solve for `b`.

`y= (-1/4) x + b`

`3= (-1/4)(7) +b`

`3= (-7/4) + b`

`12/4= (-7/4) + b`

Add `(7/4)` to both sides

`b = (19/4)`

Plug b into the slope intercept equation

`y= -1/4x + 19/4`