Use the image to answer the question.

Question

Two coordinate planes show one graphed line each. The solid line on the left slopes downward from left to right. The dotted line on the right slopes upward from left to right. The first coordinate plane shows a solid line that has a y-intercept at coordinates left parenthesis 0 comma 5 right parenthesis, has an x-intercept at coordinates left parenthesis 2.5 comma 0 right parenthesis, and continues to coordinates at left parenthesis 5 comma negative 5 right parenthesis. The second coordinate plane shows a dotted line that passes through coordinates at left parenthesis negative 5 comma negative 5 right parenthesis, has an x-intercept at left parenthesis negative 2.5 comma 0 right parenthesis, and has a y-intercept at coordinates left parenthesis 0 comma 5 right parenthesis. On the coordinate plane, both axes range from negative 5 to 5.

Compare the linear additive relationship shown in the graphs. Determine if the relationship shows (1) parallel lines, (2) perpendicular lines, (3) both parallel and perpendicular lines, or (4) neither parallel nor perpendicular lines. Enter the number of the correct answer.

(1 point)

Answer 1

To determine the relationship between the two lines based on their slopes, we first need to find the slopes of each line.

1. Solid Line (left):

   • Points: The y-intercept is (0, 5) and the x-intercept is (2.5, 0).
   • The slope (m) can be calculated using the formula:
     \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
   • Using the points (0, 5) and (2.5, 0): \[ m = \frac{0 - 5}{2.5 - 0} = \frac{-5}{2.5} = -2 \]

2. Dotted Line (right):

   • Points: The y-intercept is (0, 5) and the x-intercept is (-2.5, 0).
   • Again, using the slope formula: \[ m = \frac{0 - 5}{-2.5 - 0} = \frac{-5}{-2.5} = 2 \]

Now we have the slopes:

• Solid Line: slope = -2
• Dotted Line: slope = 2

Next, we check if the lines are parallel or perpendicular.

• Parallel Lines: Two lines are parallel if their slopes are equal. Here, the slopes are -2 and 2, which are not equal. Therefore, the lines are not parallel.

• Perpendicular Lines: Two lines are perpendicular if the product of their slopes equals -1. \[ (-2) \times (2) = -4 \quad (\text{not } -1) \] Hence, the lines are not perpendicular.

Based on these analyses, the lines show (4) neither parallel nor perpendicular lines.

Final answer: 4