Question

How do you calculate the slope, x intercept, and y intercept of the following equation: `3x + 4y= 0`?

Answer 1

Slope = -3/4
The x intercept is 0
The y intercept is 0

Explanation:

Method 1 : Convert to slope intercept form
`color(white)("XXXX")`A linear equation in the form:
`color(white)("XXXX")` `color(white)("XXXX")` `y = mx+b`
`color(white)("XXXX")`is in slope intercept form with slope `=m`
`color(white)("XXXX")`and y-intercept `=b`
`3x+4y = 0`

`rarr 4y = -3x + 0`

`rarr y = -3/4x+0` `color(white)("XXXX")`(slope intercept form with slope `-3/4` and y intercept `= 0`
Substituting `y=0` into the original equation gives `x=0`, the x-intercept.

Method 2: Use the slope formula for a standard form linear equation
`color(white)("XXXX")`A linear equation in standard form:
`color(white)("XXXX")` `color(white)("XXXX")` `Ax+By=C`
`color(white)("XXXX")`has a slope of `-(A/B)`
`color(white)("XXXX")`or, in this case
`color(white)("XXXX")` `color(white)("XXXX")`-3/4#

The y-intercept is the value of y when `x=0`
`rarr` y intercept `= 0`

The x-intercept is the value of x when `y=0`
`rarr` x intercept `=0`