How do you find the slope and intercept of x= 2y+2?

Mar 18, 2016

$\textcolor{b l u e}{{y}_{\text{intercept}} = - 1}$
$\textcolor{b l u e}{{x}_{\text{intercept}} = 2}$
$\textcolor{b l u e}{\text{Gradient } = + 2}$

Explanation:

$\textcolor{b r o w n}{\text{It does not matter if you have "x=2y+2" or by }}$
$\textcolor{b r o w n}{\text{manipulation "y=x/2-1 ". They both plot the same }}$$\textcolor{b r o w n}{\text{straight line.}}$

So the slope $\textcolor{b l u e}{\text{(gradient) is 2}}$. That is: for every 1 along you go up 2. You always read from left to right for the gradient.

+2 means the line goes up whilst -2 means it goes down!
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color(blue)("To determine "x_("intercept"))

The line will cross the x-axis at y=0

Set y=0 giving:

$x = 2 \left(0\right) + 2$

$\textcolor{b l u e}{{x}_{\text{intercept}} = 2}$

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color(blue)("To determine "y_("intercept"))

The line will cross the y-axis at x=0

Set x=0 giving:

$0 = 2 y + 2$

Subtract $\textcolor{red}{2}$ from both sides

$0 \textcolor{red}{- 2} = 2 y + 2 \textcolor{red}{- 2}$

$- 2 = 2 y + 0$

Divide both sides by $\textcolor{red}{2}$

$- \frac{2}{\textcolor{red}{2}} = \frac{2}{\textcolor{red}{2}} \times y$

But $\frac{2}{- 2} = - 1 \text{ and } \frac{2}{2} = + 1$

$- 1 = 1 \times y$

$\textcolor{b l u e}{{y}_{\text{intercept}} = - 1}$
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