# How do you find the slope and y intercept for y = -2x + 7?

Jan 3, 2016

$\textcolor{p u r p \le}{\text{Look at the very detailed method used/explained in my solution.}}$

#### Explanation:

$\textcolor{b l u e}{\text{Slope or gradient}}$
The slope is the amount of up or down for the amount of along and is directly related to the change in $x$ and the change in $y$.
So if you had say, 6 down (change in y value) for 3 along (change in x value) the slope is $\textcolor{w h i t e}{. .} \left(6 \text{ up or down")/(3 " along}\right)$
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But if we treat this as a ratio and divide both numerator and denominator by 3 we have:

$\frac{6 \div 3}{3 \div 3} = \frac{2}{1} = 2$

So for every 1 along we have 2 up or down.
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We need to have a way of showing if the slop is upwards or downwards. The convention for this is that if we have -2 then the slope is downwards if we move from left to right. In which case +2 means upwards.
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$\textcolor{b r o w n}{\text{So your question has a downward slop of } - 2}$
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$\textcolor{b l u e}{\text{x intercept}}$
This is when the line crosses the x-axis. The x-axis it at $y = 0$
So to find this we substitute $y = 0 \text{ into } y = - 2 x + 7$ giving:

$0 = - 2 x + 7$
Add $2 x$ to both sides giving:
$0 + 2 x = 2 x - 2 x + 7$
$2 x = 0 + 7$
Divide both sides by 2 giving:
$\frac{2}{2} x = \frac{7}{2}$
$1 \times x = \frac{7}{2} = 3 \frac{1}{2}$
color(brown)(x_("intercept")= 3 1/2
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$\textcolor{b l u e}{\text{y intercept}}$

This when the line crosses the y-axis. The y-axis is at $x = 0$. So we substitute $x = 0$ into $y = - 2 x + 7$ giving

$y = \left(2 \times 0\right) + 7$

color(brown)(y_("intercept")= 7
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