Question

what is the slope of the line?
$2x + 4y = 6x - y$
choose 1 answer:
a $\frac{5}{4}$
b $\frac{3}{2}$
c $\frac{4}{5}$
d $\frac{2}{3}$

Explanation:

Step1: Rearrange the equation to slope - intercept form ($y = mx + b$)

We start with the equation $2x + 4y=6x - y$. First, we want to get all the $y$ terms on one side and the $x$ terms on the other side. Add $y$ to both sides of the equation:
$2x + 4y+y=6x - y + y$, which simplifies to $2x + 5y=6x$.
Then, subtract $2x$ from both sides:
$2x-2x + 5y=6x - 2x$, so $5y = 4x$.

Step2: Solve for $y$

Divide both sides of the equation $5y = 4x$ by $5$ to get $y$ by itself. Using the formula $y=\frac{4}{5}x+0$ (in the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept). The coefficient of $x$ is the slope.

Answer:

C. $\frac{4}{5}$