I am suppose to do a graph using these numbers: 6x - 2y = 2 9x - 3y = 1 but I cannot get the graph link to come up any suggestions.
To plot the graph of these two equations, you can follow these steps:
Step 1: Solve each equation for y to get them in slope-intercept form (y = mx + b).
For the first equation, 6x - 2y = 2, rearrange it to get:
-2y = -6x + 2 (subtract 6x from both sides)
y = 3x - 1 (divide by -2)
For the second equation, 9x - 3y = 1, rearrange it to get:
-3y = -9x + 1 (subtract 9x from both sides)
y = 3x - 1/3 (divide by -3)
Step 2: Choose some x-values and plug them into each equation to find the corresponding y-values.
For example, you can choose x = 0, 1, and -1.
For the first equation:
- When x = 0, y = 3(0) - 1 = -1. So one point is (0, -1).
- When x = 1, y = 3(1) - 1 = 2. So another point is (1, 2).
- When x = -1, y = 3(-1) - 1 = -4. So another point is (-1, -4).
For the second equation:
- When x = 0, y = 3(0) - 1/3 = -1/3. So one point is (0, -1/3).
- When x = 1, y = 3(1) - 1/3 = 8/3. So another point is (1, 8/3).
- When x = -1, y = 3(-1) - 1/3 = -10/3. So another point is (-1, -10/3).
Step 3: Plot the points on a graph. Each point will represent an intersection of the two lines.
Step 4: Connect the plotted points with a straight line to obtain the graph for each equation.
If you're having trouble generating the graph or link, you can use graphing software or online graphing tools available. Simply enter the equations and the software/tool will plot the graph for you. Some popular graphing tools include Desmos, GeoGebra, and Wolfram Alpha.
Once you have the graph, you will be able to visually see the intersection points, if any exist, which are the solutions to the system of equations.