03Asketch-special

= Special Cases = toc

Vertical Lines (x = a)
{where a is constant}

The equation ** x = a **
 * produces a vertical line
 * has x-intercept at **(a, 0)**

{The __gradient__ of a vertical line is undefined (or infinity)}

** Example 5 **
math \textbf{(a)} \quad \text{Sketch } x = 3 math

__**Solution:**__

The line will connect all of the points where the __**x-value**__ = 3.
 * Eg:** (3, 0), (3, 3), (3, 5) etc

Plotting these points shows
 * they are all in a vertical line
 * x-intercept at ** (3, 0) **

math \textbf{(b)} \quad \text{Sketch } x = -1 math

__**Solution:**__

Produces
 * a vertical line
 * x-intercept at ** (–1, 0) **

Horizontal Lines (y = a)
{where a is constant}

Note: This can be drawn using the gradient-intercept method.
 * ** y = a ** is equivalent to **y = 0x + a**
 * y-intercept at ** a **
 * gradient = 0 so ** rise = 0 **, **run = 1**

The equation ** y = a ** produces
 * a horizontal line
 * has y-intercept at ** (0, a) **

{The gradient of a horizontal line is 0}

** Example 6 **
math \textbf{(a)} \quad \text{Sketch } y = 1 math

__**Solution:**__ The line will connect all the points where the __**y-value**__ = 1
 * Eg:** (–2, 1), (0, 1), (3, 1) etc

Plotting these points shows
 * they are all in a horizontal line
 * y-intercept at ** (0, 1) **

math \textbf{(b)} \quad \text{Sketch } y = -2 math

__**Solution:**__

Produces
 * a horizontal line
 * y-intercept at ** (0, –2) **

Sketch y = x
Note: This can be drawn using the gradient-intercept method.
 * ** y = x ** is equivalent to **y = 1x + 0**
 * y-intercept at ** 0 **
 * gradient = 1 so ** rise = 1 **, **run = 1**

{If the scale is the same on each axis, a gradient of 1 produces a line at 45º above the horizontal}



** Example 7 **
math \text{Sketch } y = x math

__**Solution:**__

The line will connect all the points where __**x-value**__ = __**y-value**__ Eg: (0, 0), (1, 1), (2, 2), etc

Plotting these points shows
 * a diagonal line 45º above the horizontal
 * y-intercept at 0

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