To identify the slope and y-intercept from the equation \(y - 6 = -2x\), we'll first rewrite it in the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the given equation:
\[ y - 6 = -2x \]
Add 6 to both sides to isolate \(y\):
\[ y = -2x + 6 \]
From this equation, we can identify:
- The slope \(m = -2\)
- The y-intercept \(b = 6\)
This means the line slopes downwards (since the slope is negative) and crosses the y-axis at (0, 6).
Graph the Linear Equation
- Plot the y-intercept: Start by plotting the point (0, 6) on the y-axis.
- Use the slope to find another point: The slope of -2 can be interpreted as: for every 1 unit you move to the right (positive x-direction), move 2 units down (negative y-direction).
- From (0, 6), if you move 1 unit to the right (to 1, 6) and then move down 2 units, you would end up at (1, 4).
- Plot this point: So plot (1, 4).
- Draw the line: Connect these two points with a straight line and extend it in both directions.
Summary
- Slope: -2
- Y-Intercept: (0, 6)
- The graph will show a straight line passing through the y-axis at (0, 6) and having a downward slope.
You can visualize it as follows:
7 | * (0,6)
6 |
5 |
4 | * (1,4)
3 |
2 |
1 |
0 |________________
0 1 2 3 4 x
The line will continue to slope down as you move to the right.