Question

y = -2x - 2
y = x + 1
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Plot \( y = -2x - 2 \)

Find two points on the line. When \( x = 0 \), \( y = -2(0) - 2 = -2 \), so the point is \( (0, -2) \). When \( x = -1 \), \( y = -2(-1) - 2 = 0 \), so the point is \( (-1, 0) \). Plot these two points and draw a line through them.

Step2: Plot \( y = x + 1 \)

Find two points on the line. When \( x = 0 \), \( y = 0 + 1 = 1 \), so the point is \( (0, 1) \). When \( x = 1 \), \( y = 1 + 1 = 2 \), so the point is \( (1, 2) \). Plot these two points and draw a line through them.

(Note: Since this is a graphing task, the final answer here is the graphical representation of the two lines. If we were to find the intersection point (solution of the system), we can solve the equations:

Set \( -2x - 2 = x + 1 \)

Step3: Solve for \( x \)

\( -2x - x = 1 + 2 \)

\( -3x = 3 \)

\( x = -1 \)

Step4: Solve for \( y \)

Substitute \( x = -1 \) into \( y = x + 1 \), \( y = -1 + 1 = 0 \). So the intersection point is \( (-1, 0) \).)

Answer:

The two lines are plotted with intersection at \( (-1, 0) \) (if solving the system) or the graphical lines as per the steps above.