Question

How do you find the slope given `x+9y=18`?

Answer 1

See a solution process below:

Explanation:

This equation is in the Standard Linear Form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

`color(red)(1)x + color(blue)(9)y = color(green)(18)`

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

Substituting gives a slope of:

`m = -color(red)(1)/color(blue)(9)`

Answer 2

`"slope "=-1/9`

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"`

`"rearrange "x+9y=18" into this form"`

`"subtract x from both sides"`

`cancel(x)cancel(-x)+9y=-x+18`

`rArr9y=-x+18`

`"divide all terms by 9"`

`(cancel(9) y)/cancel(9)=-1/9x+2`

`rArry=-1/9x+2larrcolor(red)"in slope-intercept form"`

`rArr"slope m"=-1/9`