Question

What is the slope intercept form of the line passing through `(3,2)` with a slope of `7/5`?

Answer 1

`y=7/5x-11/5`

Explanation:

First use the Point Slope form of a line:

`(y-color(blue)(y_1)) = color(green)m(x-color(blue)(x_1))`

`(y-color(blue)(2)) = color(green)(7/5)(x-color(blue)(3))`

Now do the algebra to convert it to slope intercept form:

`y-2=7/5x-21/5`

`y=7/5x-21/5+2`

`y=7/5x-21/5+10/5`

`y=7/5x-11/5`

graph{y-2=7/5x-21/5 [-10, 10, -5, 5]}

Answer 2

`y=7/5x-11/5`

Explanation:

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

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"here "m=7/5`

`y=7/5x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(3,2)" into the partial equation"`

`2=21/5+brArrb=10/5-21/5=-11/5`

`y=7/5x-11/5larrcolor(red)"in slope-intercept form"`