Question

How do you find the standard, point-slope, and slope intercept forms given m= -4/3, b=5/3?

Answer 1

Slope Intercept Form
`y=-4/3x+5/3`
Point-Slope Form
`y-5/3=-4/3(x-0)`
Standard Form
`4x+3y=5`

Explanation:

Slope Intercept Form
`y=mx+b`
`y=-4/3x+5/3`
Point-Slope Form
`y-y_1=m(x-x_1)`
We know that the `y`-intercept is `(0,5/3)`, so we already know a point on the line.
`y-5/3=-4/3(x-0)`
Standard Form
`ax+by=c`
We can start off by using slope-intercept form, and then just solve for the constant (the integer).
`y=-4/3x+5/3`
`4/3x+y=5/3` add `4/3` to both sides
`4x+3y=5` Multiply the whole equation by 3 to achieve integer coefficients for every term (which is what standard form calls for)