Answer :
To graph the equation [tex]\(y + 2 = \frac{1}{2}(x + 2)\)[/tex], follow these steps:
1. Convert the Equation to Slope-Intercept Form (y = mx + b):
- Start with the given equation:
[tex]\[ y + 2 = \frac{1}{2}(x + 2) \][/tex]
- Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right-hand side:
[tex]\[ y + 2 = \frac{1}{2} x + 1 \][/tex]
- Subtract 2 from both sides to isolate [tex]\(y\)[/tex]:
[tex]\[ y = \frac{1}{2} x + 1 - 2 \][/tex]
- Simplify the equation:
[tex]\[ y = \frac{1}{2} x - 1 \][/tex]
2. Identify the Slope and Y-Intercept:
- The equation [tex]\(y = \frac{1}{2} x - 1\)[/tex] is now in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- The slope ([tex]\(m\)[/tex]) is [tex]\(\frac{1}{2}\)[/tex].
- The y-intercept ([tex]\(b\)[/tex]) is -1.
3. Find Points to Plot:
- When [tex]\(x = 0\)[/tex]:
- Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[ y = \frac{1}{2}(0) - 1 = -1 \][/tex]
- Point: [tex]\((0, -1)\)[/tex]
- When [tex]\(x = 2\)[/tex]:
- Substitute [tex]\(x = 2\)[/tex] into the equation:
[tex]\[ y = \frac{1}{2}(2) - 1 = 1 - 1 = 0 \][/tex]
- Point: [tex]\((2, 0)\)[/tex]
- When [tex]\(x = -2\)[/tex]:
- Substitute [tex]\(x = -2\)[/tex] into the equation:
[tex]\[ y = \frac{1}{2}(-2) - 1 = -1 - 1 = -2 \][/tex]
- Point: [tex]\((-2, -2)\)[/tex]
4. Plot the Points on the Graph:
- Plot the points [tex]\((0, -1)\)[/tex], [tex]\((2, 0)\)[/tex], and [tex]\((-2, -2)\)[/tex] on the coordinate plane.
5. Draw the Line:
- Connect the plotted points with a straight line, extending the line through the points.
The graph should show a straight line passing through the points [tex]\((0, -1)\)[/tex], [tex]\((2, 0)\)[/tex], and [tex]\((-2, -2)\)[/tex], with a slope of [tex]\(\frac{1}{2}\)[/tex] and a y-intercept of -1.
1. Convert the Equation to Slope-Intercept Form (y = mx + b):
- Start with the given equation:
[tex]\[ y + 2 = \frac{1}{2}(x + 2) \][/tex]
- Distribute the [tex]\(\frac{1}{2}\)[/tex] on the right-hand side:
[tex]\[ y + 2 = \frac{1}{2} x + 1 \][/tex]
- Subtract 2 from both sides to isolate [tex]\(y\)[/tex]:
[tex]\[ y = \frac{1}{2} x + 1 - 2 \][/tex]
- Simplify the equation:
[tex]\[ y = \frac{1}{2} x - 1 \][/tex]
2. Identify the Slope and Y-Intercept:
- The equation [tex]\(y = \frac{1}{2} x - 1\)[/tex] is now in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- The slope ([tex]\(m\)[/tex]) is [tex]\(\frac{1}{2}\)[/tex].
- The y-intercept ([tex]\(b\)[/tex]) is -1.
3. Find Points to Plot:
- When [tex]\(x = 0\)[/tex]:
- Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[ y = \frac{1}{2}(0) - 1 = -1 \][/tex]
- Point: [tex]\((0, -1)\)[/tex]
- When [tex]\(x = 2\)[/tex]:
- Substitute [tex]\(x = 2\)[/tex] into the equation:
[tex]\[ y = \frac{1}{2}(2) - 1 = 1 - 1 = 0 \][/tex]
- Point: [tex]\((2, 0)\)[/tex]
- When [tex]\(x = -2\)[/tex]:
- Substitute [tex]\(x = -2\)[/tex] into the equation:
[tex]\[ y = \frac{1}{2}(-2) - 1 = -1 - 1 = -2 \][/tex]
- Point: [tex]\((-2, -2)\)[/tex]
4. Plot the Points on the Graph:
- Plot the points [tex]\((0, -1)\)[/tex], [tex]\((2, 0)\)[/tex], and [tex]\((-2, -2)\)[/tex] on the coordinate plane.
5. Draw the Line:
- Connect the plotted points with a straight line, extending the line through the points.
The graph should show a straight line passing through the points [tex]\((0, -1)\)[/tex], [tex]\((2, 0)\)[/tex], and [tex]\((-2, -2)\)[/tex], with a slope of [tex]\(\frac{1}{2}\)[/tex] and a y-intercept of -1.
