To find the x- and y-intercepts of the line given by the equation \( y = \frac{5}{4}x \), we can follow these steps:
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Finding the y-intercept: The y-intercept occurs when \( x = 0 \). So we substitute \( x = 0 \) into the equation:
\[ y = \frac{5}{4}(0) = 0 \]
Therefore, the y-intercept is at the point \( (0, 0) \).
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Finding the x-intercept: The x-intercept occurs when \( y = 0 \). So we set \( y = 0 \) in the equation and solve for \( x \):
\[ 0 = \frac{5}{4}x \]
To solve for \( x \), we multiply both sides by \( \frac{4}{5} \):
\[ x = 0 \]
Thus, the x-intercept is also at the point \( (0, 0) \).
In conclusion, both the x-intercept and y-intercept of the line \( y = \frac{5}{4}x \) are at the point \( (0, 0) \).