Solve the following system of equations graphically on the set of axes below.
y, equals, x, plus, 6
y=x+6
y, equals, minus, start fraction, 3, divided by, 2, end fraction, x, minus, 4
y=−
2
3
​
x−4
Plot two lines by clicking the graph.
Click a line to delete it.
x
y
x
y
Answer
Attempt 1 out of 2

Solution:  Submit Answer

To solve this system of equations graphically, we need to plot the two lines represented by the equations and find their point of intersection. Here's the step-by-step process:

### Step 1: Write down the given equations
- Equation 1: \( y = x + 6 \)
- Equation 2: \( y = -\frac{3}{2}x - 4 \)

### Step 2: Plot the first equation \( y = x + 6 \)
- This is a straight line with a slope of 1 and a y-intercept of 6. 
- To plot the line:
  1. Start at the point (0, 6) on the y-axis (because when \( x = 0 \), \( y = 6 \)).
  2. Use the slope of 1 (which means for every increase of 1 in \( x \), \( y \) also increases by 1). From the point (0, 6), move up 1 unit and right 1 unit to find another point, (1, 7). Repeat for other points if needed.

### Step 3: Plot the second equation \( y = -\frac{3}{2}x - 4 \)
- This line has a slope of \( -\frac{3}{2} \) and a y-intercept of -4.
- To plot the line:
  1. Start at the point (0, -4) on the y-axis (because when \( x = 0 \), \( y = -4 \)).
  2. Use the slope of \( -\frac{3}{2} \) (which means for every increase of 2 in \( x \), \( y \) decreases by 3). From the point (0, -4), move down 3 units and right 2 units to find another point, (2, -7). Repeat for other points if needed.

### Step 4: Find the intersection point
- The solution to the system of equations is where the two lines intersect. Plot both lines and look for the point where they cross.

Once you've plotted the lines, identify the coordinates of the intersection point. This point will give you the solution to the system of equations in the form \( (x, y) \).

Let me know if you'd like me to calculate the intersection point algebraically or if you have any other questions!

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Here are 5 related questions to consider:
1. How can you solve a system of equations algebraically using substitution or elimination?
2. What does the slope of a line tell you about its steepness and direction?
3. How can you determine if two lines are parallel or perpendicular by looking at their slopes?
4. How do you interpret the solution of a system of equations geometrically?
5. What are the possible outcomes when solving systems of linear equations graphically (one solution, no solution, or infinitely many solutions)?

**Tip:** When graphing lines, always make sure to plot at least two points correctly and check the slope to ensure accuracy!

Solve the following system of equations graphically on the set of axes below. y = x + 6 y = −(3/2)x − 4

Learn how to solve the system of linear equations y = x + 6 and y = −(3/2)x − 4 graphically. This lesson covers essential concepts like graphing lines using slope and y-intercept and finding the intersection point. Ideal for students in Grades 8-10.

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