Question

What is the slope and a point on the line of `y - 9 = -3/4(x-4)`?

Answer 1

See below.

Explanation:

The slope of the line is just `-frac(3)(4)` (rise over run), as it is the coefficient of the `x`-term. A point on the line can be found by plugging in some real value of `x`, and then solving for `y`.

For example, say `x=4`.

Then, `y-9=-frac(3)(4)(4-4)`, `y=9+0=9` so one point `(x,y)` on the line is `(4,9)`.

Answer 2

`"slope "=-3/4" and point "=(4,9)`

Explanation:

The equation of a line in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`y-9=-3/4(x-4)" is in this form"`

and by comparison of the 2 equations.

`m=-3/4" and a point on the line "=(4,9)`