Straight Line Graphs
Maths: Edexcel IGCSE Higher, topic 3.3.2
Straight Line Graphs
Any straight line can be written as y = mx + c.
y = mx + c
- m is the gradient of the line
- c is the y-intercept (the height of the point where the line crosses the y axis.
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Parallel lines have the same gradient
- y = 3x + 2 and y = 3x - 4 are parallel lines because they have the same gradient (3).
Gradient and y-intercept of a Line
A line y = mx + c has gradient m and y-intercept c.
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y-intercept
- The point where a line crosses the y-axis is called the y-intercept.
Gradient
- To calculate the gradient (slope) of a line, use 2 co-ordinates (A and B):
- gradient = change in y ÷ change in x
- where change in y = (yA - yB) and change in x = (xA - xB)
Midpoint of a Line
The midpoint of a line is the point that lies the same distance from each of the endpoints.
Midpoint
- To calculate the coordinates of the midpoint between points A and B, work out the horizontal distance between A & B and add half of this to the x-coordinate of A.
- This is the x-coordinate of the midpoint.
- Do the same for the vertical distance to get the y-coordinate.
Midpoint formulae
- The coordinates of the midpoint of a line AB are given by the formulae above.
Test yourself on Straight Line Graphs
Show that the lines y = 7x + 5 and y = 7x - 3 are parallel.
Show that the lines y = -2x + 1 and y = -2x + 3 are parallel.
Are the lines y = 3.5x - 17 and y = 3.5x -1.5 parallel, vertical or perpendicular?
Are the lines y = 2x + 17 and y = 2x -1.5, parallel, vertical or perpendicular?
Which of these describes the lines y = 2 and y = 5?