Straight Line Graphs

Understanding Straight Line Graphs

  • A straight line graph is visual representation of a linear equation.
  • The general equation for a straight line is y = mx + c, where ‘m’ is the gradient and ‘c’ is the y-intercept.

Calculating Gradient

  • The gradient or slope of a line is calculated as rise over run.
  • In an equation, ‘m’ represents the gradient. If ‘m’ is positive, the line slopes upwards. If ‘m’ is negative, it slopes downwards.
  • A larger absolute value of ‘m’ means a steeper slope.

Identifying the Y-Intercept

  • The y-intercept, represented as ‘c’ in the equation, is the point where the line crosses the y-axis.
  • It is the y-coordinate of the point where the line intersects with the y-axis.

Plotting Linear Equations

  • To plot a linear graph, start by marking the y-intercept on the y-axis.
  • Then use the gradient to determine the direction and steepness of the line.

Finding Equations of Straight Lines

  • Given any two points on a line, you can find the line’s equation.
  • First, calculate the gradient using the coordinates of the two points.
  • Then use a point and the gradient in the equation y - y1 = m(x - x1) to find ‘c’, the y-intercept.

Horizontal and Vertical Lines

  • Horizontal lines have a gradient of zero and are of the form y = c where ‘c’ is a constant.
  • Vertical lines have an undefined gradient and are of the form x = c where ‘c’ is a constant.

Parallel and Perpendicular Lines

  • Two lines are parallel if they have the same gradient.
  • Two lines are perpendicular if the product of their gradients is -1. If one line has a gradient ‘m’, the other line will have a gradient of -1/m.