Linear Function y=mx+b Practice Problems & Solutions

For this problem, we need to determine the nature of the slope for a given straight line on a graph.

Based on the graph provided, the red line starts at a higher point on the left (Y-axis) and moves downward toward a lower point on the right (X-axis). This indicates that as one moves from left to right across the graph, the function decreases in value. Consequently, this is typical of a line that has a negative slope.

The slope of a line is typically defined as the "rise over the run," or the ratio of the change in the vertical direction to the change in the horizontal direction. Here, as we proceed from left to right, the line goes "downwards" (negative rise), establishing a negative slope.

Thus, we can conclude that the slope of the line is negative.

Therefore, the solution to the problem is Negative slope.

To solve this problem, follow these steps:

• Step 1: Observe the given graph and the plotted line.
• Step 2: Determine the direction of the line as it moves from left to right across the graph.
• Step 3: Understand that a line moving downwards from left to right represents a negative slope.

Now, let's work through these steps:

Step 1: The graph shows a straight line that starts higher on the left side and descends towards the right side.

Step 2: As the line moves from left to right, it descends. This is a key indicator of the slope type.

Step 3: A line that moves downward from the left side to the right side of the graph (decreasing in height as it proceeds to the right) is characteristic of a negative slope. Conversely, a positive slope would show a line ascending as it moves rightward.

Therefore, the solution to the problem is the line has a negative slope.

To determine the slope of the line, we'll examine the direction of the line segment on the graph:

• The line depicted moves from the top left, passing through a point with higher $y$-coordinate values, to the bottom right, ending at a point with lower $y$-coordinate values.
• This movement indicates that as $x$ increases (the direction to the right along the $x$-axis), the $y$-coordinate decreases.
• When the $y$-value reduces as the $x$-value grows, the slope $m$ is negative.

Since the line descends from left to right, the slope of the line is negative.

Therefore, the slope of the function is a negative slope.

To determine the slope of the line segment shown in the graph, follow these steps:

• Identify the line segment on the graph; it's shown as a red line from one point to another.
• Examine the direction the line segment travels from the leftmost point to the rightmost point.
• Visually analyze whether the line segment is rising or falling as it moves from left to right.

Here is the detailed analysis:
- The red line segment starts lower on the left side and ends higher on the right side.
- This suggests that as we move from left to right, the line is rising.
- In terms of slope, a line that rises as it moves from left to right has a positive slope.

Therefore, the slope of the line segment is positive.

Thus, the correct answer is Positive slope.

To solve this problem, let's evaluate the graph of the line provided:

• The line is visually represented as starting from the bottom left to the top right, moving upwards.
• In a standard Cartesian graph, a line that ascends as it progresses from left to right implies a positive change in the y-coordinate as the x-coordinate increases.
• This upward trajectory indicates that the slope, $m$, is positive.

Thus, the slope of the function is positive.

Therefore, the answer is Positive slope.