# How do you graph y = -5x + 2  using the slope and intercept?

Feb 15, 2017

$\underline{\text{Full explanation given using first principles.}}$
The calculations become quite fast once you get used to them and start using shortcuts.

#### Explanation:

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

Where m is the gradient (slope)

This is the amount of up or down for a given amount along

The y-intercept is where $x = 0$ which is the value of $c$
The x-intercept is where $y = 0$
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$\textcolor{b l u e}{\text{Determine the gradient}}$

Directly comparing $y = - 5 x + 2$ to the above we have:

Gradient (slope)$= m = - 5$
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$\textcolor{b l u e}{\text{Determine the y intercept}}$

y_("intercept") " is at " x=0 " "->y=-5(0)+2" "=" "2" "=" "c

Full coordinate for ${y}_{\text{intercept}} \to \left(x , y\right) = \left(0 , 2\right)$
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$\textcolor{b l u e}{\text{Determine the x intercept}}$

x_("intercept")" is at "y=0

$\implies \text{ "y=-5x+2" " ->" } \textcolor{g r e e n}{0 = - 5 x + 2}$

Add $\textcolor{red}{5 x}$ to both sides

$\textcolor{g r e e n}{0 \textcolor{red}{+ 5 x} = - 5 x \textcolor{red}{+ 5 x} + 2}$

$5 x = 0 + 2$

$\textcolor{g r e e n}{5 x = 2}$

Divide both sides by $\textcolor{red}{5}$

$\textcolor{g r e e n}{\frac{5}{\textcolor{red}{5}} x = \frac{2}{\textcolor{red}{5}}}$

${x}_{\text{intercept}} = \frac{2}{5}$

Full coordinate for ${x}_{\text{intercept}} \to \left(x , y\right) = \left(\frac{2}{5} , 0\right)$