To rewrite the given equation of the line \(\(2x + y = 4\)\) in slope-intercept form, we can follow these steps:
1. Rewrite the equation in the form \(\(y = mx + b\)\):
- Start with the given equation: \(\(2x + y = 4\)\).
- To isolate \(\(y\)\), subtract \(\(2x\)\) from both sides of the equation:
\(\[
y = -2x + 4
\]\)
2. Identify the slope (m) and y-intercept (b):
- From the rewritten equation \(\(y = -2x + 4\)\), we can see that:
- The slope (\(\(m\)\)) is \(\(-2\)\).
- The y-intercept (\(\(b\)\)) is \(\(4\)\).
Now, let's state the solution clearly:
- Slope: \(\(-2\)\)
- Y-intercept: \(\(4\)\)
Graphing the Line:
1. Plot the y-intercept: Start by plotting the point where the line crosses the y-axis. For this equation, the y-intercept is \(\(4\)\). So, plot the point \(\((0, 4)\)\) on the graph.
2. Use the slope to find another point:
- The slope of \(\(-2\)\) means that for every 1 unit you move to the right along the x-axis, you move 2 units down along the y-axis.
- From the y-intercept \(\((0, 4)\)\), move 1 unit to the right to \(\((1, ?)\)\).
- From \(\((1, ?)\)\), move 2 units down to \(\((1, 2)\)\).
3. Plot this second point: Now, plot the point \(\((1, 2)\)\) on the graph.
4. Draw the line: Finally, draw a straight line through the points \(\((0, 4)\)\) and \(\((1, 2)\)\). This line represents the equation \(\(y = -2x + 4\)\).
By following these steps, you have rewritten the equation in slope-intercept form, identified the slope and y-intercept, and graphed the line correctly.
