Solve the following system of equations graphically on the set of axes below.
y, equals, start fraction, 3, divided by, 2, end fraction, x, minus, 4
y= 
2
3
​
 x−4
y, equals, minus, one third, x, plus, 7
y=− 
3
1
​
 x+7

To solve this system of equations graphically, we need to plot both equations on the same set of axes and determine where the lines intersect. The solution to the system will be the point where both lines meet.

Here are the two equations:

1. \( y = \frac{3}{2}x - 4 \)
2. \( y = -\frac{1}{3}x + 7 \)

### Step 1: Graph the first equation \( y = \frac{3}{2}x - 4 \)
- The slope is \( \frac{3}{2} \), meaning for every 2 units moved horizontally, the line goes up by 3 units.
- The y-intercept is -4, so the line crosses the y-axis at \( (0, -4) \).
- From \( (0, -4) \), move 2 units to the right and 3 units up to plot a second point. Continue this process to get more points if needed.

### Step 2: Graph the second equation \( y = -\frac{1}{3}x + 7 \)
- The slope is \( -\frac{1}{3} \), meaning for every 3 units moved horizontally, the line goes down by 1 unit.
- The y-intercept is 7, so the line crosses the y-axis at \( (0, 7) \).
- From \( (0, 7) \), move 3 units to the right and 1 unit down to plot a second point. Again, you can continue this process to get more points.

### Step 3: Find the point of intersection
After plotting both lines, look for the point where they intersect. This point is the solution to the system of equations.

Would you like me to graph these lines for you or explain any step in more detail?

### 5 Related Questions:
1. How do you determine the slope of a line from its equation?
2. What does the y-intercept represent in a linear equation?
3. How can you solve a system of equations algebraically instead of graphically?
4. What are the key differences between a positive and a negative slope?
5. How do you determine whether two lines will intersect just by looking at their equations?

### Tip:
Always check the slope and y-intercept of both lines first, as this can help you sketch the graph more accurately.

Solve the following system of equations graphically on the set of axes below. y = (3/2)x - 4 and y = -(1/3)x + 7.

Learn how to solve the system of linear equations y = (3/2)x - 4 and y = -(1/3)x + 7 graphically. This step-by-step solution guides you through plotting both lines and finding their intersection. Suitable for Grades 9-10 students studying Algebra and Systems of Equations.

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