Question

In the standard (x, y) coordinate plane, what is the slope of the line with equation 7y - 3x = 21?

Answer 1

See a solution process below:

Explanation:

We can rewrite this equation in standard 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

`-3x + 7y = 21`

`color(red)(-1)(-3x + 7y) = color(red)(-1) xx 21`

`(color(red)(-1) xx -3x) + (color(red)(-1) xx 7y) = -21`

`3x + (-7y) = -21`

`color(red)(3)x + color(blue)(-7)y = color(green)(-21)`

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

Substituting gives:

`m = (-color(red)(3))/color(blue)(-7) = 3/7`

Answer 2

`Slope = m = 3/7`

Explanation:

`7y-3x=21`

This equation is in standard form `ax+by=c`

To find the slope of the equation, we want the equation in slope-intercept from `y=mx+b` where `m` is the slope

Begin by rearranging the equation to equal `y`

`7ycolor(red)(-3x)=21`

`3x` is being subtracted, so perform the opposite operation of addition to get `3x` on the other side of the equation

`7y=color(red)(3x)+21`

Isolate `y` by dividing the opposite side of the equation by `7`

`color(blue)(7y)=3x+21`

`color(blue)((7y)/7)=(3x)/color(blue)(7)+21/color(blue)7`

`y=3/7x+3`

Now the equation is in slope-intercept form

`y=color(green)(3/7)x+3`

`y=color(green)mx+b`

Remember, `m` is the slope

`Slope = m = 3/7`