Question
Graph the equation and identify the \( y \)-intercept. \( y=\frac{1}{4} x \)
Ask by Luna Sandoval. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The \( y \)-intercept is at \( (0, 0) \). To graph the equation \( y = \frac{1}{4}x \), start at \( (0, 0) \) and move right 4 units and up 1 unit to plot another point, then draw a straight line through these points.
Solution
1. Write the equation in slope-intercept form:
\[
y = \frac{1}{4}x + 0
\]
2. The \( y \)-intercept of a line in the form \( y = mx + b \) is given by the point \( (0, b) \). Here, \( b = 0 \).
3. Thus, the \( y \)-intercept is:
\[
(0, 0)
\]
4. To graph the equation, start at the \( y \)-intercept \( (0, 0) \). Since the slope is \( \frac{1}{4} \), for every 4 units you move to the right, you move up 1 unit. Plot additional points using this slope and draw a straight line through them.
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Simplify this solution Mind Expander
To graph the equation \( y = \frac{1}{4} x \), start by plotting the y-intercept. Since there’s no constant term added, the y-intercept (where \( x = 0 \)) is \( (0, 0) \). Next, find another point by choosing a simple value for \( x \). For \( x = 4 \), \( y = \frac{1}{4} \cdot 4 = 1 \), giving you the point \( (4, 1) \). Draw a straight line through the points \( (0, 0) \) and \( (4, 1) \). The y-intercept of this linear equation is \( (0, 0) \), where the line crosses the y-axis, proving that sometimes the easiest points are the most vital!
