Question

to graph the equation $2x + 5y = 10$, zeplyn draws a line through the points $(5, 0)$ and $(0, 2)$. what is the slope of the line represented by $2x + 5y = 10$?

$\circ\\ \boldsymbol{ -\frac{5}{2} }$

$\circ\\ \boldsymbol{ -\frac{2}{5} }$

$\circ\\ \boldsymbol{ \frac{2}{5} }$

$\circ\\ \boldsymbol{ \frac{5}{2} }$

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

We have the points \( (5, 0) \) (so \( x_1 = 5, y_1 = 0 \)) and \( (0, 2) \) (so \( x_2 = 0, y_2 = 2 \)).

Step3: Substitute into the slope formula

Substitute the values into the formula: \( m=\frac{2 - 0}{0 - 5}=\frac{2}{-5}=-\frac{2}{5} \).

Answer:

\(-\frac{2}{5}\) (corresponding to the option with this value)