To find the \( x \)-intercept of a line, we use the information that the line passes through the origin \((0, 0)\) and has a slope of \(\frac{2}{5}\).
The equation of a line can be expressed in the slope-intercept form:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the \( y \)-intercept. Since the line passes through the origin, the \( y \)-intercept \( b = 0\). Therefore, the equation of the line simplifies to:
\[ y = \frac{2}{5}x \]
Next, to find the \( x \)-intercept, we set \( y = 0 \) and solve for \( x \):
\[ 0 = \frac{2}{5}x \]
To isolate \( x \), we multiply both sides by \(\frac{5}{2}\):
\[ 0 \cdot \frac{5}{2} = x \quad \Rightarrow \quad x = 0 \]
Thus, the \( x \)-intercept of the line is
\[ \boxed{0} \]
8 answers