To identify the y-intercept of the equation \( y = \frac{1}{4}x - 3 \), we can set \( x = 0 \) and solve for \( y \).
Substituting \( x = 0 \) into the equation:
\[ y = \frac{1}{4}(0) - 3 \]
\[ y = -3 \]
So, the y-intercept is \( (0, -3) \).
Y-intercept: \( -3 \)
Now, to graph the equation \( y = \frac{1}{4}x - 3 \):
- Start by plotting the y-intercept at the point \( (0, -3) \).
- The slope of the line is \( \frac{1}{4} \), which means for every 4 units you move to the right (increasing \( x \)), you move up 1 unit (increasing \( y \)).
From the y-intercept:
- Move 4 units right to \( x = 4 \) and then 1 unit up to \( y = -2 \) to get the point \( (4, -2) \).
- You could also move left from the y-intercept: 4 units left to \( x = -4 \) and then down 1 unit to find \( ( -4, -4) \).
Plot these points and draw a straight line through them.
The line should extend in both directions, with a positive slope indicating it goes upward from left to right. That completes the graph of the equation \( y = \frac{1}{4}x - 3 \).
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