Question

Graph and then find the solution for y=-1/2x-6

Answer 1

To solve the equation \( y = -\frac{1}{2}x - 6 \), we'll first graph the equation and then find the solution points.

### Step 1: Identify the components for graphing

The equation is in slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope, which is \( -\frac{1}{2} \).
- \( b \) is the y-intercept, which is \( -6 \).

### Step 2: Plot the y-intercept

Start by plotting the y-intercept:
- The y-intercept is at \( (0, -6) \).

### Step 3: Use the slope to find another point

From the y-intercept, apply the slope:
- The slope \( -\frac{1}{2} \) means that for each 2 units you move to the right (positive x-direction), you move down 1 unit (negative y-direction).

Starting from the point \( (0, -6) \):
- Move 2 units to the right to \( (2, -6) \).
- Move 1 unit down to \( (2, -7) \).

Thus, the second point is \( (2, -7) \).

### Step 4: Draw the graph

Plot both points \( (0, -6) \) and \( (2, -7) \) on a graph and draw a straight line through them. This line represents the equation \( y = -\frac{1}{2}x - 6 \).

### Step 5: Finding solutions

Since the equation describes a line, any point \( (x, y) \) that lies on this line is a solution to the equation.

If you want specific values of \( x \) and \( y \), you can choose any \( x \) value and solve for \( y \):
- **Example 1**: If \( x = 0 \):
\[
y = -\frac{1}{2}(0) - 6 = -6
\]
So, \( (0, -6) \) is a solution.

- **Example 2**: If \( x = 2 \):
\[
y = -\frac{1}{2}(2) - 6 = -1 - 6 = -7
\]
So, \( (2, -7) \) is a solution.

- **Example 3**: If \( x = 4 \):
\[
y = -\frac{1}{2}(4) - 6 = -2 - 6 = -8
\]
So, \( (4, -8) \) is another solution.

### Conclusion

The graph is a straight line with a negative slope and a y-intercept at \( -6 \). Any point on this line is a solution to the equation \( y = -\frac{1}{2}x - 6 \).