Question

lines meet. our y-intercept first and then use the slope to rewrite the equation into y=mx+b form or 2) =0) to plot two points and create the line. 2) $y = -\frac{1}{2}x - 1$ $y = x - 4$ 4) $y = \frac{1}{4}x + 2$ $y = \frac{5}{4}x - 2$

Explanation:

To find the intersection point of the two lines \( y = -\frac{1}{2}x - 1 \) and \( y = x - 4 \), we can set the two equations equal to each other since they both equal \( y \).

Step 1: Set the equations equal

Set \( -\frac{1}{2}x - 1 = x - 4 \)

Step 2: Solve for \( x \)

Add \( \frac{1}{2}x \) to both sides:
\( -1 = x + \frac{1}{2}x - 4 \)
Combine like terms:
\( -1 = \frac{3}{2}x - 4 \)

Add 4 to both sides:
\( 3 = \frac{3}{2}x \)

Multiply both sides by \( \frac{2}{3} \):
\( x = 3 \times \frac{2}{3} = 2 \)

Step 3: Find \( y \)

Substitute \( x = 2 \) into \( y = x - 4 \):
\( y = 2 - 4 = -2 \)

Answer:

The lines intersect at the point \( (2, -2) \)