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.