Question

What is the equation of the line that has a slope of `m=3/4` and goes through `(5,2)`?

Answer 1

`y=3/4x-7/4`

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"`

`"here "m=3/4" and " (x_1,y_1)=(5,2)`

`rArry-2=3/4(x-5)larrcolor(red)" in point-slope form"`

Distributing the bracket and simplifying gives an alternative version of the equation.

`y-2=3/4x-15/4`

`rArry=3/4x-15/4+2`

`rArry=3/4x-7/4larrcolor(red)" in slope-intercept form"`