Straight Lines and Gradients

Understanding Straight Lines and Gradients

Terminology

• Gradient: explains how steep a line is. It’s calculated by dividing the vertical change by the horizontal change between any two points.
• Y-intercept: the place where the line crosses the y-axis.
• Equation of a straight line: shown as y = mx + c, where m is the gradient and c is the y-intercept.

Finding the Gradient

• Gradient of vertical lines is undefined.
• If two vertical lines are parallel, their gradients are the same.
• To calculate the gradient, take two points on the line (x1, y1) and (x2, y2). Then use the formula (y2 - y1) / (x2 - x1).
• For a line going uphill from left to right, the gradient is positive.
• For a line going downhill from left to right, the gradient is negative.

Straight Line Equations

• A straight line equation describes all points on that line.
• Use the formula y = mx + c to calculate. ‘m’ refers to the gradient and ‘c’ to the y-intercept.
• The y-intercept ‘c’ is the value of y when x = 0.
• If you know the gradient and a point on the line, you can substitute these into the formula to find the y-intercept.

Graphing Straight Lines

• Draw a line using its equation by plotting the y-intercept first and then using the gradient to draw the rest of the line.
• Plot more points using the line equation if needed.
• For increasing lines, as x gets bigger, so does y.
• For decreasing lines, as x gets bigger, y decreases.

Real World Applications

• Understanding gradients and straight line equations are vital for solving real-world problems, including rates of change and interpreting graphs.
• Fields that rely on these principles include physics, engineering, computer science and economics.

In all topics, remember to always check your work and ensure your answers make sense in the context of the question.