Question

find the slope of the line and sketch the graph. 3x - 5y = 15 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slope is \\(\square\\) (type an integer or a simplified fraction.) b. the slope is undefined.

Explanation:

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

We start with the equation $3x - 5y=15$. We want to solve for $y$.
First, subtract $3x$ from both sides of the equation:
$- 5y=-3x + 15$

Step2: Solve for y

Divide each term in the equation $-5y=-3x + 15$ by $- 5$:
$y=\frac{-3x}{-5}+\frac{15}{-5}$
Simplify each term:
$y = \frac{3}{5}x-3$
In the slope - intercept form $y = mx + b$, the coefficient of $x$ (i.e., $m$) is the slope. So the slope $m=\frac{3}{5}$.

Answer:

$\frac{3}{5}$