Question
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Graph the equation and identify the \( y \)-intercept. \( y=\frac{1}{4} x \)

Ask by Herrera Vargas. in the United States
Mar 14,2025

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Tutor-Verified Answer

Answer

The \( y \)-intercept is at \((0,0)\).

Solution

1. The given equation is \[ y = \frac{1}{4}x. \] 2. To find the \( y \)-intercept, set \( x = 0 \): \[ y = \frac{1}{4}(0) = 0. \] Thus, the \( y \)-intercept is at the point \((0,0)\). 3. To graph the equation, note that it is a straight line with a slope of \(\frac{1}{4}\) and a \( y \)-intercept at \((0,0)\). For example: - When \( x = 4 \): \[ y = \frac{1}{4}(4) = 1, \] giving the point \((4,1)\). - When \( x = -4 \): \[ y = \frac{1}{4}(-4) = -1, \] giving the point \((-4,-1)\). 4. Plotting these points and drawing a straight line through them completes the graph of the equation.

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Bonus Knowledge

To graph the equation \( y = \frac{1}{4} x \), start by plotting the \( y \)-intercept, which is the point where the line crosses the \( y \)-axis. In this case, since there is no constant term added to the equation, the \( y \)-intercept is at the origin, \( (0, 0) \). Next, you can determine another point by choosing a value for \( x \) (e.g., \( x = 4 \)), which gives you \( y = \frac{1}{4}(4) = 1 \). Plot the point \( (4, 1) \), and draw a straight line through these points to complete the graph. The \( y \)-intercept is \( (0, 0) \) in this equation, indicating that when \( x \) is 0, \( y \) is also 0. This point is essential in understanding the line's behavior across the Cartesian plane.

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