Drawing Straight Line Graphs

Drawing Straight Line Graphs

Straight Line Graphs Overview

  • A straight line graph in algebra is a linear equation that takes the form y = mx + c. This is also referred to as the equation of a straight line.
  • In this equation, ‘m’ represents the gradient or slope of the line and ‘c’ represents the y-intercept, the point where the line crosses the y-axis.

Determining the Gradient and Y-Intercept

  • The gradient, or m, of a line indicates its steepness. A positive gradient slopes upwards from left to right, while a negative gradient slopes downwards.
  • The y-intercept, or c, is the point on the line where it intersects the y-axis, when x equals 0.

Drawing Straight Line Graphs

  • Coordinate axes are drawn using horizontal and vertical lines, typically referred to as x and y axes.
  • Plot the y-intercept first on your graph. This provides a starting point for your line.
  • The gradient then determines how to draw your line from the y-intercept. If the gradient is 2, for example, move 2 units up for every 1 unit you move to the right.

Straight Line Graph Characteristics

  • Straight line graphs are always linear and do not curve. They can either be an increasing or decreasing line based on the sign of the gradient.
  • When the gradient is zero, the line is horizontal. When the line is vertical, the gradient is undefined or sometimes referred to as infinite.

Various Forms of Straight Line Equation

  • The standard form of a straight line equation is y = mx + c. However, straight line equations may also be presented in other forms like slope-intercept form (y = mx + b), point-slope form (y - y1 = m(x - x1)), or intercept form (x/a + y/b = 1).

Revision and Practice

  • Proficiency in drawing straight line graphs requires continuous practice. This involves identifying gradients, y-intercepts and familiarizing oneself with different forms of straight line equations.
  • Utilize different sets of coordinates in practice to build versatility in sketching straight line graphs.

Understanding straight line graphs is central to grasping the broader concepts of Algebra. Therefore, you should aim to master this skill.