2.2 Equations of Straight Lines

• Gradient of a line
• Equation of a straight line
• Equation of a straight line in the form y = mx + c
• The x and y intercepts of a straight line

• identify the gradient in real-life situations
• determine the gradient of a line from two known points
• determine the equation of a straight line given two points
• determine the equation of a straight line from a known point and a gradient
• express the equation of a straight line in the form y = mx + c
• interpret the equation y = mx + c in different situations
• determine the x and y intercepts of a straight line
• recognise the use of equations of straight lines in real life

“How do we use gradient or steepness in our daily activities?”

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1. Steepness we can see
   40 min · 1 practice tasks · quiz
   Steepness is something you already judge by eye and by effort; gradient is the number that records it.
2. Gradient as rise over run
   40 min · 1 practice tasks · quiz
   Gradient is the rise divided by the run, and on a straight line it is the same wherever you measure it.
3. Gradient from two known points
   40 min · 1 practice tasks · quiz
   Subtract the y values and the x values in the same order, then divide, to get the gradient.
4. Positive, negative, zero and undefined
   40 min · 1 practice tasks · quiz
   The sign of the gradient says whether a line rises or falls; flat lines give zero and vertical lines have none.
5. Gradients on a building site
   40 min · 1 practice tasks · quiz
   Builders write gradients as 1 in 12 or as a percentage; both are the same rise over run.
6. A line from one point and a gradient
   40 min · 1 practice tasks · quiz
   One point and a gradient fix exactly one line, and y - y1 = m(x - x1) writes down its equation.
7. A line through two points
   40 min · 1 practice tasks · quiz
   Find the gradient from the two points first, then use either point to write the equation.
8. The form y = mx + c
   40 min · 1 practice tasks · quiz
   When an equation is arranged as y = mx + c, the gradient and the starting value can be read straight off.
9. What m and c do to the line
   40 min · 1 practice tasks · quiz
   Changing m tilts the line about its intercept; changing c slides the line up or down.
10. Rearranging into y = mx + c
    40 min · 1 practice tasks · quiz
    Make y the subject by moving the x term and dividing every term, then read off m and c.
11. The y-intercept
    40 min · 1 practice tasks · quiz
    Where a line crosses the y-axis, x is zero; substitute x = 0 to find the intercept.
12. The x-intercept
    40 min · 1 practice tasks · quiz
    Where a line crosses the x-axis, y is zero; set y = 0 and solve for x.
13. Sketching a line from its intercepts
    40 min · 1 practice tasks · quiz
    Find where the line crosses each axis, plot those two points and join them with a ruler.
14. Straight-line stories: charges and rates
    40 min · 1 practice tasks · quiz
    Many real charges are a fixed amount plus a steady rate, which is exactly y = mx + c.
15. Gradients and lines at work in Kenya
    40 min · 1 practice tasks · quiz
    Pull the sub-strand together: gradient, equation, intercepts and what they mean in real situations.