The image shows a question on slopes of lines in a coordinate plane, focusing on lines $e$ and $f$, with slope values of $-1$ and $1$. The question asks which of the provided statements is true.

Let's break it down:

1. Line slopes:

   • Line $e$ is decreasing from left to right, meaning its slope is negative, specifically $-1$.
   • Line $f$ is increasing from left to right, meaning its slope is positive, specifically $1$.

2. Evaluating the answer options:

   • Option 1: "Lines $e$ and $f$ have the same steepness, so it makes sense that their slopes are the same distance from 0 on a number line."

     • This is true because the absolute value of both slopes is 1, so both lines have the same steepness.

   • Option 2: "Line $e$ has a slope of $-1$ because it is going down from left to right, which means line $f$ has a slope of $1$."

     • This is correct as well. The direction of the lines corresponds to their slopes.

   • Option 3: "Line $e$ has a slope of $-1$ because it is the most steep, which means line $f$ has a slope of 1."

     • This is incorrect because both lines have the same steepness (slope magnitude of 1), so line $e$ is not steeper than line $f$.

   • Option 4: "Two of these are true."

     • This is correct because both Option 1 and Option 2 are true.

Correct Answer:

The correct selection is Option 4 ("Two of these are true") because both the first and second statements are valid.

Would you like further details on this or have any questions? Here are five related questions to deepen your understanding:

1. How is slope calculated for a line on a coordinate plane?
2. What does it mean if two lines have the same steepness but different slopes?
3. How do you determine whether a slope is positive or negative?
4. What is the relationship between perpendicular lines and their slopes?
5. How can you visually identify the slope of a line from a graph?

Tip: The slope of a line is essentially its steepness and direction. Positive slopes rise to the right, and negative slopes fall to the right.