# 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.