# How do you find the slope of (1,5), (-8,2)?

Jun 28, 2016

Slope = $\frac{1}{3}$

#### Explanation:

To find the slope for any 2 points $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$, you use the following formula:

slope formula: $m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$

For our case, points are (1,5) and (-8,2)

slope $m = \frac{5 - 2}{1 - \left(- 8\right)}$ = $\frac{3}{9} = \frac{1}{3}$

Jun 28, 2016

The gradient (slope) is $\frac{1}{3}$

#### Explanation:

Like the gradient on a hill, the slope (gradient) is the amount of change in the up or down for the given amount of along as you read from left to right.

Let the gradient be $m$

$m = \left(\text{change in up or down")/("change in along")->("change in y")/("change in x}\right)$

I have reversed the order of your points so that the $x$ values read left to right.

Let the first point be $\text{ } {P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(\textcolor{b r o w n}{- 8 , 2}\right)$
Let the second point be ${P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(\textcolor{b l u e}{1 , 5}\right)$

$m = \frac{\textcolor{b l u e}{{y}_{2}} \textcolor{b r o w n}{- {y}_{1}}}{\textcolor{b l u e}{{x}_{2}} \textcolor{b r o w n}{- {x}_{1}}} = \frac{\textcolor{b r o w n}{\textcolor{b l u e}{5} - 2}}{\textcolor{b l u e}{1} \textcolor{b r o w n}{- \left(- 8\right)}}$

But $1 - \left(- 8\right)$ is the same as $1 + 8$
Note that 2 minuses is the same as a plus.

$m = \frac{5 - 2}{1 + 8} = \frac{3}{9}$

But $\frac{3}{9} \equiv \frac{3 \div 3}{9 \div 3} \equiv \frac{1}{3}$

So the gradient (slope) is $\frac{1}{3}$

This means that if you move to the right by 3 you have gone up 1
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$\textcolor{b l u e}{\text{Additional Teaching bit}}$
Suppose the gradient had been $- \frac{1}{3}$

This would mean that you go to the right by 3 but you go down 1.

Negative gradient is a downward slope ( left to right)
Positive gradient is an upward slop (left to right)