## Equation of a straight line

### Gradient form

The general equation for a straight line in its gradient form is:

where *m *= the gradient of the line

*c = *a constant

If we let *x* = 0, then it is found that *y = c*. Therefore *c *is equal to the *y*-intercept.

#### Application

*Sketch the graph of the equation y = 2x + 3.*

Firstly, *c* = 3 and therefore the *y*-intercept is at the point (0, 3).

To find the *x*-intercept, let *y* = 0. The *x*-intercept is therefore at (-3/2, 0).

Plot both of these points and join them to create the line.

### Intercept form

Another way to express a linear relation is in the form:

where *a, b,* and *c* are all constants

This is referred to as the intercept form as it is convenient in determining the *x* and *y* intercepts.

#### Application

*Sketch the graph 8x + 11y = 88.*

When *x* = 0, *y = *8. Therefore the *y-*intercept is at (0, 8).

When *y = 0*, *x* = 11. Therefore the *x*-intercept is at (11, 0).

## Finding the equation of a straight line

The gradient, *m*, of the line can be rearranged using a general point *(x, y) *on the same line

This form is most convenient when determining the equation of a straight line.

### Given two points

When two points of a line are found, they can be substituted into the gradient formula in order to find the slope, *m*. After that, the re-arranged gradient formula can be used for convenience.

*Find the equation of the straight line passing through the points (6, 4) and (2, -4).*

The gradient must first be found:

This value, as well as any of the given points can be substituted into the formula:

### Given a point, and the gradient

Using the same re-arranged formula, the equation can be quickly deduced.

*Find the equation of the line that passes through the point (2,5) and has a gradient of -3. *

Using

### Given a graph

In a graph, the value of *c* reads as the y-intercept. *m* is the gradient and can be calculated using two points on the line. The equation can therefore be written in the form *y = mx + c*

**See also:**

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