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