On grid paper, draw the grahp of y=4x and the graph of y=-4x on the same set of axes. How are the graphs alike? How are they different
Graph them. I suspect one goes up, and one down.
To graph the equations y=4x and y=-4x on the same set of axes, we need to follow a few steps:
Step 1: Set up a grid paper with the x-axis (horizontal) and y-axis (vertical) intersecting at the origin (0,0).
Step 2: Determine the range of values you want to plot on the graph. Generally, you choose x-values that would show a good representation of the graph.
Step 3: Plot points on the graph by substituting different x-values into the equations and calculating the corresponding y-values.
For y=4x:
- For x=0, y=4(0)=0, giving us the point (0,0) on the graph.
- For x=1, y=4(1)=4, giving us the point (1,4) on the graph.
- For x=-1, y=4(-1)=-4, giving us the point (-1,-4) on the graph.
- Continue this process to plot more points if desired.
For y=-4x:
- For x=0, y=-4(0)=0, giving us the point (0,0) on the graph.
- For x=1, y=-4(1)=-4, giving us the point (1,-4) on the graph.
- For x=-1, y=-4(-1)=4, giving us the point (-1,4) on the graph.
- Continue this process to plot more points if desired.
Step 4: Connect the points on the graph using straight lines. Since we are dealing with linear equations, the lines will be straight.
Now that we have the graphs plotted, let's analyze how they are alike and different:
Similarities:
- Both graphs pass through the origin (0,0) because when x=0, y will always be 0 for both equations.
Differences:
- The slope of the line for y=4x is positive (+4), indicating that it goes up as x increases.
- The slope of the line for y=-4x is negative (-4), indicating that it goes down as x increases.
- The line y=4x is steeper compared to the line y=-4x since the absolute value of its slope is greater.
- The line y=4x is in the first and third quadrants, while the line y=-4x is in the second and fourth quadrants.
Visually, the graph of y=4x will form an increasing line passing through the origin, and the graph of y=-4x will form a decreasing line passing through the origin.