Linear Graphs

What the number tells you

• The gradient measures how steep a line is and which way it slopes
• A gradient of 3 means the line rises 3 for every 1 step to the right, and a gradient of −4 means it falls 4 for every 1 step to the right
• An uphill line, running from bottom left to top right, has a positive gradient; a downhill line has a negative one
• Comparing steepness ignores the sign, so a gradient of −5 is steeper than one of 2
• A horizontal line has gradient 0, and a vertical line has no gradient at all because there is no horizontal step to divide by

Measuring it

• On a printed grid, pick two points that sit on the line and complete a right-angled triangle between them

• The gradient is the vertical change divided by the horizontal change
• Choose two points that sit exactly on grid intersections and are far apart, because a short triangle magnifies any reading error
• Read the scales before counting squares: the two axes often use different scales, and one square is frequently not one unit
• Put the minus sign back in yourself for a downhill line, since the counting gives only the size