To graph the line represented by the equation \( y = \frac{1}{4}x - 4 \), you'll want to identify the y-intercept and the slope.
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Y-Intercept: This is the point where the line crosses the y-axis. From the equation \( y = \frac{1}{4}x - 4 \), we can see that the y-intercept is \(-4\). So, the point is (0, -4).
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Slope: The slope is given by the coefficient of \( x \), which is \(\frac{1}{4}\). This means that for every 4 units you move to the right (positive direction along the x-axis), the line moves up 1 unit (positive direction along the y-axis).
Using this information, let's plot two points:
- Start at the y-intercept: (0, -4).
- From here, use the slope: Move 4 units to the right (to x = 4) and 1 unit up (to y = -3). This gives you another point: (4, -3).
Now you have two points: (0, -4) and (4, -3).
Draw a line through these points; this line represents the equation \( y = \frac{1}{4}x - 4 \).
If you want to plot additional points for more accuracy, you can use the slope again:
- Starting from (4, -3), move right 4 (to 8) and up 1 (to -2), marking the point (8, -2).
- You can also find points to the left of (0, -4). For example, move left 4 units to (-4), and because the slope is \(\frac{1}{4}\), to remain on the line, you would move down 1 unit to (-4, -5).
With these points plotted, you can draw a straight line through them to represent your linear equation.
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