Question

What is the equation of the line with slope `m= -7/17` that passes through `(2,1)`?

Answer 1

`7x+17y=31`

Explanation:

In slope-point form:
`color(white)("XXX")y-color(red)(y')=color(green)(m)(x-color(blue)(x'))`
for a line with slope `color(green)(m)` through the point `(color(blue)(x'),color(red)(y'))`

GIven `color(green)(m=-7/17)` and the point `(color(blue)(x'),color(red)(y'))=(color(bue)(2),color(red)(1))`

`color(white)("XXX")y-color(red)(1)=color(green)(-7/17)(x-color(blue)(2))`

Converting to standard form:
`color(white)("XXX")17y-17=-7x+14`

`color(white)("XXX")7x+17y=31`