# Exercise 13.1 class 8 solution

### Exercise 13.1 class 8 solution- a linear graph

A linear graph is a graphical representation of a linear relationship between two variables. In a linear relationship, the relationship between the variables can be expressed by a straight line on a graph. Here are some key characteristics and properties of linear graphs:

1. Linearity: A linear graph represents a linear relationship, meaning that as one variable changes, the other changes at a constant rate. In mathematical terms, this relationship can be expressed as y = mx + b, where “y” is the dependent variable, “x” is the independent variable, “m” is the slope (a constant that determines the rate of change), and “b” is the y-intercept (the value of “y” when “x” is zero).
2. Straight Line: The graph of a linear relationship is a straight line on a Cartesian coordinate system. This line passes through the origin (0, 0) if the y-intercept “b” is zero.

### Exercise 13.1 class 8 solution -exercise preview

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### Exercise 13.1 class 8 solution – solution pdf

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13.1

Exercise 4.1 class 8 solution

Exercise 3.2 class 8 solution

Exercise 2.3 class 8 solution

Exercise 1.1 class 8 solution

### Exercise 13.1 class 8 solution-steps in plotting a graph

Plotting a graph in mathematics involves a series of steps to visually represent data or functions. Here are the general steps to follow:

1. Gather Data or Define a Function:
• If you have data points to plot, collect the data and organize it into pairs or sets of values.
• If you are graphing a function, make sure you understand the equation or relationship that you want to graph.
2. Choose the Appropriate Coordinate System:
• Decide whether you need a two-dimensional (2D) or three-dimensional (3D) graph based on the nature of your data or function.
• For 2D graphs, you’ll typically use a Cartesian coordinate system with two perpendicular axes (x and y).
• For 3D graphs, you’ll use a 3D Cartesian coordinate system with three perpendicular axes (x, y, and z).
3. Label the Axes:
• Label the x-axis and y-axis (or x, y, and z axes in 3D) with appropriate scales and units. Make sure the labels are clear and descriptive.
4. Determine the Scale:
• Decide the scale at which you’ll represent values on the axes. This scale will depend on the range of your data or function and the size of your graph.
5. Plot Data Points or Evaluate the Function:
• For data points, use the coordinates provided to plot the points on the graph.
• For functions, evaluate the function for different values of the independent variable (x) and plot corresponding points.
6. Connect Data Points (Optional):
• If you have data points, consider connecting them with straight lines or curves to show trends or relationships.
• If you’re graphing a function, you can plot a smooth curve based on the values you calculated.
7. Label Points and Curves (Optional):
• Label data points or curves if necessary, especially if you want to indicate specific values or distinguish between multiple lines on the same graph.
• Title the graph to provide context and describe what it represents.
• Label the axes with their names and units.

### Exercise 13.1 class 8 solution- location of point

The location of points in a coordinate system is a fundamental concept in mathematics and geometry. Points are used to represent specific positions in space, and their locations are typically described using a coordinate system. There are two common types of coordinate systems: the Cartesian coordinate system and the polar coordinate system.

1. Cartesian Coordinate System:
• In a Cartesian coordinate system, points are located using two perpendicular axes, typically labeled as the x-axis and the y-axis. These axes intersect at a point called the origin (usually labeled as O).
• Each point in this system is represented by an ordered pair (x, y), where “x” is the distance along the x-axis, and “y” is the distance along the y-axis.
• The x-coordinate (abscissa) indicates how far to the right (positive) or left (negative) a point is from the origin.
• The y-coordinate (ordinate) indicates how far up (positive)
• or down (negative) a point is from the origin.
• Example: The point (3, 4) represents a location 3 units to the right and 4 units up from the origin.