Question

question image (a coordinate grid with two red lines plotted)

Explanation:

To analyze the two lines in the graph, we can find their equations and then determine their relationship (e.g., parallel, perpendicular, intersecting). Let's assume we need to find the slopes of the two lines.

Step 1: Identify points on each line

For the left line (let's call it Line 1):

• It passes through \((0, -2)\) and \((-1, 0)\) (we can also use other points, but these are clear from the grid).

For the right line (Line 2):

• It passes through \((0, 2)\) and \((1, 0)\).

Step 2: Calculate the slope of Line 1

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

For Line 1, using points \((0, -2)\) (\(x_1 = 0, y_1 = -2\)) and \((-1, 0)\) (\(x_2 = -1, y_2 = 0\)):
\[
m_1 = \frac{0 - (-2)}{-1 - 0} = \frac{2}{-1} = -2
\]

Step 3: Calculate the slope of Line 2

Using points \((0, 2)\) (\(x_1 = 0, y_1 = 2\)) and \((1, 0)\) (\(x_2 = 1, y_2 = 0\)):
\[
m_2 = \frac{0 - 2}{1 - 0} = \frac{-2}{1} = -2
\]

Step 4: Analyze the slopes

Since \(m_1 = m_2 = -2\), the two lines are parallel (they have the same slope and different y - intercepts, so they never intersect and are parallel).

If the question was to find if the lines are parallel, the answer is yes, as their slopes are equal. If it was to find the slope, the slope of each line is \(-2\).

Assuming the question is about the slope or parallelism:

Answer:

The two lines have a slope of \(\boldsymbol{-2}\) and are parallel.