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Coordinates and straight-line graphs
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Coordinates fix points on a grid. Every straight-line graph has an equation that links x and y.
Coordinates in four quadrants
(x, y): go across first, then up or down.
(−3, 5) is 3 left and 5 up. (4, −2) is 4 right and 2 down.
The x-axis is the line y = 0; the y-axis is the line x = 0.
(−3, 5) is 3 left and 5 up. (4, −2) is 4 right and 2 down.
The x-axis is the line y = 0; the y-axis is the line x = 0.
Horizontal and vertical lines
y = 6 is a horizontal line: every point on it has y-coordinate 6.
x = −3 is a vertical line: every point on it has x-coordinate −3.
x = −3 is a vertical line: every point on it has x-coordinate −3.
Plotting y = 2x + 1
Make a table of values, plot the points and join them with a ruler.
If a point fits the equation, it lies on the line: (3, 7) is on y = 2x + 1 because 2 × 3 + 1 = 7.
If a point fits the equation, it lies on the line: (3, 7) is on y = 2x + 1 because 2 × 3 + 1 = 7.
Does the point (4, 10) lie on the line y = 3x − 2?
- Substitute x = 4: y = 3 × 4 − 2 = 10
- The y-coordinate is 10, which matches
Answer: Yes
Coordinates are (across, up). y = a is horizontal and x = a is vertical. A point lies on a line if its coordinates fit the equation.
The interactive lesson includes the diagrams for this topic.
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