Question

How do you write an equation of a line given point (3,7) and slope 2/7?

Answer 1

`y=2/7x+43/7`

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=2/7`

`rArry=2/7x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(3,7)" into the partial equation"`

`7=6/7+brArrb=49/7-6/7=43/7`

`rArry=2/7x+43/7larrcolor(red)"equation of line"`

Answer 2

`y = (2x)/7 + 43/7` (form: y = mx + c)

`2x - 7y + 43 = 0` (form: ax + by + c = 0)

Either are acceptable answers. Your teacher may prefer a certain form.

Explanation:

By the Point-Slope Form, (which, by the way, is a method of computing the equation of a line given its slope and a point on it):

`(y - y_1) = m(x - x_1)` where `m` is the slope and `(x_1, y_1)` is the coordinates of the given point.
`(y - 7) = 2/7 (x- 3)`
`(y - 7) = (2x)/7 - 6/7`
`y = (2x)/7 +43/7`