# How do you graph y = 1/2x- 6 using the slope and intercept?

May 22, 2017

See explanation.

A lot of method detail given. The actual calculation is a lot faster than given once you are used to equations of this type.

#### Explanation:

Given: $y = \frac{1}{2} x - 6$

Compare to the standardised form of $y = m x + c$

$\textcolor{b l u e}{\text{Teaching bit about gradient}}$

Where m->" gradient"->("change in y")/("change in x")

Note that the gradient is consequential to reading left to write on the x-axis. This is important as it indicates if the graph is like 'going up a hill' or if it is like 'going down a hill' left to right.

Negative gradient is going down $y \to \text{ becomes less}$
Positive gradient is going up $y \to \text{ becomes greater}$

So we have $m = \left(\text{change in y")/("change in x}\right) \to \frac{1}{2}$

As this is positive the graph 'goes up' reading left to right.

$m = \left(\text{change in y")/("change in x}\right) \to \frac{1}{2}$ means that for every change of 1 in the y-axis the x-axis changes by 2.
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$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{b r o w n}{\text{Determine the y-intercept}}$

The plot crosses the y-axis at $x = 0$ so by substitution we have:

${y}_{\text{intercept}} = \frac{1}{2} \left(0\right) - 6$

${y}_{\text{intercept}} = 0 - 6$

${y}_{\text{intercept}} = - 6$

y_("intercept")->(x,y)=(0,-6) color(green)(" Notice "-6" is the constant"
$\text{ } \textcolor{g r e e n}{\downarrow}$
$\text{ } y = m x \textcolor{g r e e n}{+ c}$

$\textcolor{b r o w n}{\text{Determine the x-intercept}}$

The plot crosses the x-axis at $y = 0$ so by substitution we have:

$0 = \frac{1}{2} {x}_{\text{intercept}} - 6$

$6 = \frac{1}{2} {x}_{\text{intercept}}$
$12 = {x}_{\text{intercept}}$
${x}_{\text{intercept}} \to \left(x , y\right) = \left(12 , 0\right)$