GCSE(F), GCSE(H),

The **gradient**, or slope, of a straight line is given by `frac(text(up))(text(along))`. In the example below, the line moves 6 up for each 2 along, and the gradient is `frac(6)(2)` = 3.

A gradient can be positive or negative. A line falling from left to right gives a negative gradient:

For each 2 along, the line falls by 3. This gives a gradient of `frac(-3)(2)` = -1.5. If a gradient is zero, it is horizontal. If a gradient is divided by 0, then it is vertical.

A straight line can be written as *y* = *mx* + *c*: *m* is the gradient, *c* is the **intercept** on the *y*-axis:

The gradient of the line is `frac(2)(1)` = 2, which is the *m* in *y* = *mx* + *c*. The *c* is where the line crosses *x* = 0: in this example the line crosses *x* = 0 with a value of *y* = 3. The equation is *y* = 2*x* + 3.

1. What is the gradient and intercept of the line *y* = *-4x* - *3*?

Answer: The gradient is -4; the intercept is -3

Using *y* = *mx* + *c*, *m* = -4 and *c* = -3.

2. Two points on a line are (0, 4) and (1, 7). What is the equation of the line?

Answer: *y* = 3*x* + 4

The gradient is `frac(3)(1)`: the line moves up 3 for each 1 along. This gives the *m* value as *y* = 3*x* + *c*.

For the intercept: when *x* = 0, *y* = 4, 4 = 3 x 0 + *c* therefore *c* = 4.

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