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- Straight-line graphs: y = mx + c
Straight-line graphs: y = mx + c
Every straight line can be described by its steepness and where it crosses the y-axis.
Gradient and intercept
In y = mx + c, m is the gradient and c is the y-intercept.
y = 2x + 3 crosses the y-axis at (0, 3) and goes up 2 for every 1 across.
y = 2x + 3 crosses the y-axis at (0, 3) and goes up 2 for every 1 across.
Gradient from two points
gradient = change in ychange in x
Through (1, 4) and (3, 10): (10 − 4)(3 − 1) = 62 = 3
Through (1, 4) and (3, 10): (10 − 4)(3 − 1) = 62 = 3
Finding the equation
Find m, then put one point into y = mx + c to find c.
m = 3, through (1, 4): 4 = 3 + c, so c = 1. Equation: y = 3x + 1.
m = 3, through (1, 4): 4 = 3 + c, so c = 1. Equation: y = 3x + 1.
Find the equation of the line through (2, 5) and (4, 9).
- m = (9 − 5)(4 − 2) = 2
- 5 = 2 × 2 + c, so c = 1
- y = 2x + 1
Answer: y = 2x + 1
y = mx + c: m is the gradient (rise over run), c is where the line crosses the y-axis. Find m from two points, then substitute a point to find c.
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