Question

there is a coordinate grid (a grid - like coordinate system with x - axis and y - axis) and two linear equations: $y = \frac{1}{2}x + 3$ and $y = -\frac{1}{2}x - 1$. (the specific question - related content may be to graph these two lines or find their intersection point, etc., but the given text mainly presents the coordinate grid and the two equations.)

Explanation:

Step1: Find intersection of two lines

To find where \( y = \frac{1}{2}x + 3 \) and \( y = -\frac{1}{2}x - 1 \) (assuming the second equation is \( y = -\frac{1}{2}x - 1 \) from the image) intersect, set them equal:
\( \frac{1}{2}x + 3 = -\frac{1}{2}x - 1 \)

Step2: Solve for x

Add \( \frac{1}{2}x \) to both sides:
\( \frac{1}{2}x+\frac{1}{2}x + 3= - 1 \)
\( x + 3=-1 \)
Subtract 3 from both sides:
\( x=-1 - 3=-4 \)

Step3: Solve for y

Substitute \( x = - 4 \) into \( y=\frac{1}{2}x + 3 \):
\( y=\frac{1}{2}(-4)+3=-2 + 3 = 1 \)

Answer:

The intersection point is \((-4,1)\)