Linear = Straight line!
So, a graph of a linear relationship is a straight line.
a line
The graph of a linear relationship takes the shape of a straight line. This line can have a positive slope, indicating a direct relationship, or a negative slope, indicating an inverse relationship. The position of the line on the graph is determined by the y-intercept, which is where the line crosses the y-axis. Overall, linear relationships exhibit a constant rate of change between the two variables involved.
To determine if a relationship is non-linear from a graph, look for patterns that do not form a straight line when plotting the data points. If the points curve or show a distinct pattern, such as a U-shape or an exponential increase, the relationship is likely non-linear. Additionally, analyzing the residuals from a linear regression can reveal non-linearity; if the residuals show a pattern rather than being randomly scattered, it indicates a non-linear relationship.
It's linear, so it's a line...
To describe a relationship given a graph, one can analyze the key features such as the shape of the graph (linear, quadratic, exponential), the direction of the trend (increasing, decreasing, constant), and any notable points (intercepts, maxima, minima). Conversely, to sketch a graph from a description, you identify the type of relationship (e.g., linear, polynomial) and its characteristics, like slopes or curvature, and then plot key points and features based on that information. Using these details, you can create an accurate representation that reflects the described relationship.
It takes the shape of a line.
It's a cartesian plane.
a line
The graph of a linear relationship takes the shape of a straight line. This line can have a positive slope, indicating a direct relationship, or a negative slope, indicating an inverse relationship. The position of the line on the graph is determined by the y-intercept, which is where the line crosses the y-axis. Overall, linear relationships exhibit a constant rate of change between the two variables involved.
To determine if a relationship is non-linear from a graph, look for patterns that do not form a straight line when plotting the data points. If the points curve or show a distinct pattern, such as a U-shape or an exponential increase, the relationship is likely non-linear. Additionally, analyzing the residuals from a linear regression can reveal non-linearity; if the residuals show a pattern rather than being randomly scattered, it indicates a non-linear relationship.
It's linear, so it's a line...
Linear.
A curved relationship is characterized by a non-linear pattern where the relationship between two variables does not follow a straight line. This means that as one variable changes, the other variable does not change at a constant rate. In contrast, a linear relationship is characterized by a straight line where the relationship between two variables changes at a constant rate. The main difference between a curved and linear relationship is the shape of the graph that represents the relationship between the variables.
To describe a relationship given a graph, one can analyze the key features such as the shape of the graph (linear, quadratic, exponential), the direction of the trend (increasing, decreasing, constant), and any notable points (intercepts, maxima, minima). Conversely, to sketch a graph from a description, you identify the type of relationship (e.g., linear, polynomial) and its characteristics, like slopes or curvature, and then plot key points and features based on that information. Using these details, you can create an accurate representation that reflects the described relationship.
to solve a linear in equality you have to write it out on a graph if the line or shape is made ou of strate lines its linear
A straight line. y=ax + b is called a linear relationship. y=ax2 + bx +c is called quadratic because the HIGHEST power of x is 2. A term with x3 would make it a cubic relationship, x4 would make it quartic and so on.
If the Object is falling at a constant velocity the shape of the graph would be linear. If the object is falling at a changing velocity (Accelerating) the shape of the graph would be exponential- "J' Shape.