Straight Line Graphs

• Straight line graphs can be identified by their linear equation, which is typically written in the form y = mx + b, where m represents the gradient (slope) of the line and b indicates the y-intercept (where the line crosses the y-axis).
• The gradient (m) of the straight line graph is the measure of the steepness of the line. A positive gradient indicates an upward slope, while a negative gradient represents a downward slope.
• The y-intercept (b) of a straight line graph signifies the point on the graph where the line crosses the y-axis. This will be the value of y when x is equal to zero.
• In order to plot a straight line graph, you first plot the y-intercept on the y-axis. From this point, use the gradient to determine the next points on the graph. For instance, a gradient of 2 means you move up 2 units for every 1 unit you move to the right.
• Straight line graphs can also be written in the form axe + by = c, where a, b and c are constants. Any horizontal line takes the form y = c, and any vertical line takes the form x = c.
• It’s essential to understand that every point on a straight line graph satisfies the equation of the line.
• Parallel lines have the same gradient but different y-intercepts. Conversely, the gradients of perpendicular lines multiply to equal -1.
• Intersections of straight-line graphs represent the solution to the system of equations represented by those lines. The x and y values at the point of intersection will satisfy both equations simultaneously.
• There are special cases to be aware of, such as horizontal lines (where m = 0 and the equation is in the form y = b) and vertical lines (which do not have a y-intercept and the equation is in the form x = a).