Types of Graphs in Math

Types of Graphs

• Linear Graphs: Straight line graphs, where the graph is a straight line.
• Quadratic Graphs: Parabolic graphs, where the graph is a U-shaped curve.
• Cubic Graphs: Graphs with a cubic equation, where the graph has a more complex shape.
• Circle Graphs: Graphs that form a circle, where every point on the graph is equidistant from a central point.
• Exponential Graphs: Graphs that show exponential growth or decay, where the graph has a rapid increase or decrease.

Drawing Graphs

• Coordinate Axes: Graphs are drawn on a pair of coordinate axes, where the x-axis is horizontal and the y-axis is vertical.
• Plotting Points: Graphs are drawn by plotting points on the coordinate axes, where each point has an x-coordinate and a y-coordinate.
• Drawing the Graph: The graph is drawn by joining the points with a line or curve, depending on the type of graph.

Geometry of Straight Lines

• Slope: The slope of a line is a measure of how steep it is, and can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
• Intercept: The intercept of a line is the point where the line crosses the y-axis, and can be calculated using the formula: y = mx + c.
• Equation of a Line: The equation of a line can be written in the form y = mx + c, where m is the slope and c is the intercept.
• Parallel and Perpendicular Lines: Two lines are parallel if they have the same slope, and two lines are perpendicular if the product of their slopes is -1.

Geometry of 2D Shapes and Construction of Geometric Figures

• Properties of 2D Shapes: 2D shapes have properties such as number of sides, number of vertices, and internal angles.
• Construction of 2D Shapes: 2D shapes can be constructed using a ruler and compass, or using a protractor and straightedge.
• Types of 2D Shapes: Common 2D shapes include triangles, quadrilaterals, polygons, and circles.
• Constructions: Geometric figures can be constructed using a variety of methods, including:
  • Bisection: Dividing a line or angle into two equal parts.
  • Perpendicular Bisector: Constructing a line perpendicular to a given line, and bisecting it.
  • Angle Construction: Constructing a specific angle using a protractor and straightedge.

Types of Graphs

• Linear Graphs are straight line graphs, where the graph is a straight line, with a constant slope.
• Quadratic Graphs are parabolic graphs, where the graph is a U-shaped curve, and the graph opens upward or downward.
• Cubic Graphs are graphs with a cubic equation, where the graph has a more complex shape, and can be increasing or decreasing.
• Circle Graphs are graphs that form a circle, where every point on the graph is equidistant from a central point, called the center of the circle.
• Exponential Graphs are graphs that show exponential growth or decay, where the graph has a rapid increase or decrease, and the rate of change is proportional to the current value.

Drawing Graphs

• Coordinate Axes are a pair of lines that intersect at a right angle, where the x-axis is horizontal and the y-axis is vertical.
• Graphs are drawn by plotting points on the coordinate axes, where each point has an x-coordinate and a y-coordinate.
• The graph is drawn by joining the points with a line or curve, depending on the type of graph, and the graph can be a continuous curve or a series of discrete points.

Geometry of Straight Lines

• The slope of a line is a measure of how steep it is, and can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where m is the slope.
• The intercept of a line is the point where the line crosses the y-axis, and can be calculated using the formula: y = mx + c, where c is the intercept.
• The equation of a line can be written in the form y = mx + c, where m is the slope and c is the intercept.
• Two lines are parallel if they have the same slope, and two lines are perpendicular if the product of their slopes is -1.

Geometry of 2D Shapes and Construction of Geometric Figures

• 2D shapes have properties such as number of sides, number of vertices, and internal angles, which can be used to classify and describe them.
• 2D shapes can be constructed using a ruler and compass, or using a protractor and straightedge.
• Common 2D shapes include triangles, quadrilaterals, polygons, and circles, each with their own unique properties.
• Geometric figures can be constructed using a variety of methods, including:
  • Bisection: Dividing a line or angle into two equal parts.
  • Perpendicular Bisector: Constructing a line perpendicular to a given line, and bisecting it.
  • Angle Construction: Constructing a specific angle using a protractor and straightedge.