# How do you find the slope given y=2/3x-8?

Feb 10, 2016

2/3

#### Explanation:

The slope (gradient) is the number in front of $x$.

As the 'coefficient' of $x \text{ is "2/3" }$then this is the slope (gradient).

Feb 10, 2016

I found: slope$= \frac{2}{3}$

#### Explanation:

Here the equation is in a particularly "friendly" form, with respect to the slope $m$, it is in Slope-Intercept form $y = m x + c$.
The slope can be read directly from your equation as $m = \frac{2}{3}$.
If you want to test it you can consider that the slope is a number that gives you how much $y$ changes with a change in $x$.
It seems difficult but you need only to choose two values of $x$ say:
${x}_{1} = 3$
${x}_{2} = 9$
and evaluate the corresponding $y$ values:
${y}_{1} = \frac{2}{3} \cdot 3 - 8 = - 6$
${y}_{2} = \frac{2}{3} \cdot 9 - 8 = - 2$
and then find the slope as:
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 2 - \left(- 6\right)}{9 - 3} = \frac{4}{6} = \frac{2}{3}$