Question

given the equation $13x + 3y = 2$, convert the equation to slope-intercept form.
$\bigcirc\\ y = -\frac{13}{3}x - \frac{2}{3}$
$\bigcirc\\ y = \frac{13}{3}x - \frac{2}{3}$
$\bigcirc\\ y = -\frac{13}{3}x + \frac{2}{3}$
$\bigcirc\\ y = \frac{13}{3}x + \frac{2}{3}$

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We need to solve the given equation $13x+3y = 2$ for $y$.

Step2: Isolate the term with y

Subtract $13x$ from both sides of the equation $13x + 3y=2$.
We get $3y=- 13x + 2$.

Step3: Solve for y

Divide each term in the equation $3y=-13x + 2$ by 3.
For the first term: $\frac{3y}{3}=y$; for the second term: $\frac{-13x}{3}=-\frac{13}{3}x$; for the third term: $\frac{2}{3}$.
So, $y =-\frac{13}{3}x+\frac{2}{3}$.

Answer:

$y =-\frac{13}{3}x+\frac{2}{3}$ (corresponding to the option: $y =-\frac{13}{3}x+\frac{2}{3}$)