# Question #e7d7d

Mar 18, 2017

See explanation

#### Explanation:

Compare to the standardised equation of a strait line $y = m x + c$

Where $m$ is the gradient (slope) and $c$ is the y-intercept.

Given:

$y = x + 1$
$y = x - 1$

Although not written the variable $m$ is there. It is of value 1.

So both lines have the same gradient (slope -> m=1)

As each 'crosses' the y-axis (y-intercept) in different places and they are parallel to each other they never cross, So there is not a common value

THUS IT IS $\underline{\text{WRONG}}$ TO STATE THAT: $\text{ } x + 1 = y = x - 1$
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I am only doing this for one of the equation. You can do the other one by following the same method.

For $y = x + 1$

Determine the x-intercept (crosses the x-axis at $y = 0$)

Set $y = 0 = x + 1$

Subtract 1 from both sides $\implies x = - 1$

Determine the y-intercept (crosses the y-axis at $x = 0$)

Set $x = 0 \to y = 0 + 1 \implies y = 1$
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