Question

How do you write an equation in standard form given point (1,9) and slope 4?

Answer 1

`y=4x+5`

Explanation:

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

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

here m = 4 and `(x_1,y_1)=(1,9)`

substitute these values into the point-slope equation.

`y-9=4(x-1)`

It is usual to distribute bracket and collect like terms.

`y-9=4x-4rArry=4x-4+9`

`rArry=4x+5" is the equation"`