Questions: Use technology to graph y1=-3x, y2=-6x, and y3=-3x+4. Compare the graphs of y2 and y3 to the graph of y1.

Transcript text: 15. Use technology to graph $y_{1}=-3 x, y_{2}=-6 x$, and $y_{3}=-3 x+4$. Compare the graphs of $y_{2}$ and $y_{3}$ to the graph of $y_{1}$.

Solution

Solution Steps

Step 1: Identify the Functions

The given functions are:

$ y_1 = -3x $
$ y_2 = -6x $
$ y_3 = -3x + 4 $

Step 2: Compare the Graphs

The graph of $ y_1 = -3x $ is a straight line passing through the origin with a slope of $-3$.
The graph of $ y_2 = -6x $ is a straight line passing through the origin with a steeper slope of $-6$, indicating it is steeper than $ y_1 $.
The graph of $ y_3 = -3x + 4 $ is a straight line parallel to $ y_1 $ but shifted upwards by 4 units.

Final Answer

The functions $ y_1 = -3x $, $ y_2 = -6x $, and $ y_3 = -3x + 4 $ are linear equations. $ y_2 $ is steeper than $ y_1 $, and $ y_3 $ is parallel to $ y_1 $ but shifted upwards.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = -3x", "y = -6x", "y = -3x + 4"], "latex_expressions": ["$y = -3x$", "$y = -6x$", "$y = -3x + 4$"]}

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