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

Mar 24, 2018

Slope Intercept Form
$y = - \frac{4}{3} x + \frac{5}{3}$
Point-Slope Form
$y - \frac{5}{3} = - \frac{4}{3} \left(x - 0\right)$
Standard Form
$4 x + 3 y = 5$

#### Explanation:

Slope Intercept Form
$y = m x + b$
$y = - \frac{4}{3} x + \frac{5}{3}$
Point-Slope Form
$y - {y}_{1} = m \left(x - {x}_{1}\right)$
We know that the $y$-intercept is $\left(0 , \frac{5}{3}\right)$, so we already know a point on the line.
$y - \frac{5}{3} = - \frac{4}{3} \left(x - 0\right)$
Standard Form
$a x + b y = c$
We can start off by using slope-intercept form, and then just solve for the constant (the integer).
$y = - \frac{4}{3} x + \frac{5}{3}$
$\frac{4}{3} x + y = \frac{5}{3}$ add $\frac{4}{3}$ to both sides
$4 x + 3 y = 5$ Multiply the whole equation by 3 to achieve integer coefficients for every term (which is what standard form calls for)