To graph the line represented by the equation [tex]\( y + 2 = \frac{1}{2}(x + 2) \)[/tex], let's follow these steps:
1. Rewrite the equation: First, we need to rewrite the equation in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
[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 solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{1}{2}x + 1 - 2
\][/tex]
[tex]\[
y = \frac{1}{2}x - 1
\][/tex]
2. Identify key points: To graph the line, we will choose two points that lie on the line.
- Let's use [tex]\( x = -10 \)[/tex] and [tex]\( x = 10 \)[/tex].
For [tex]\( x = -10 \)[/tex]:
[tex]\[
y = \frac{1}{2}(-10) - 1 = -5 - 1 = -6
\][/tex]
So, the point is [tex]\( (-10, -6) \)[/tex].
For [tex]\( x = 10 \)[/tex]:
[tex]\[
y = \frac{1}{2}(10) - 1 = 5 - 1 = 4
\][/tex]
So, the point is [tex]\( (10, 4) \)[/tex].
3. Plot the points: On a coordinate plane, plot the points [tex]\( (-10, -6) \)[/tex] and [tex]\( (10, 4) \)[/tex].
4. Draw the line: Use a ruler to draw a straight line through these two points. This line represents the equation [tex]\( y = \frac{1}{2}x - 1 \)[/tex].
5. Label the equation: Label the line on the graph with its equation [tex]\( y = \frac{1}{2}x - 1 \)[/tex].
Here is a summary of the specific points:
- Point 1: [tex]\( (-10, -6) \)[/tex]
- Point 2: [tex]\( (10, 4) \)[/tex]
By plotting these points:
[tex]\[
(-10, -6) \quad \text{and} \quad (10, 4)
\][/tex]
and drawing a line through them, you will have successfully graphed the line represented by the equation [tex]\( y + 2 = \frac{1}{2}(x + 2) \)[/tex]. The equation of the line can be written as [tex]\( y = \frac{1}{2}(x + 2) - 2 \)[/tex].
