What is the slope and intercept for $2 x + 3 y = 9$ $2x+3y=9$ and how would you graph it?

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Answer 1 · 2015-10-07T22:07:06

$m = - \frac{2}{3}$ $m=-2/3$

$c = 9$ $c=9$

A straight line graph is of the form:

$y = m x + c$ $y=mx+c$

$m$ $m$ is the gradient

$c$ $c$ is the intercept which is the point at $x = 0$ $x=0$ where the line cuts the $y$ $y$ axis.

So we get our equation into this form:

$2 x + 3 y = 9$ $2x+3y=9$

$3 y = - 2 x + 9$ $3y=-2x+9$

$y = - \frac{2}{3} x + 9$ $y=-2/3x+9$

So the slope or gradient $m = - \frac{2}{3}$ $m=-2/3$

The intercept $c = 9$ $c=9$

To graph it manually just pick a range of values of $x$ $x$ and find the corresponding value of $y$ $y$ .

e.g $x = 1 \Rightarrow$ $x=1rArr$

$y = - (\frac{2}{3} \times 1) + 9 = = \frac{25}{3}$ $y=-(2/3xx1)+9= =25/3$

So your 1st point is $[1, \frac{25}{3}]$ $[1,25/3]$

You should end up with this:

graph{-2/3x+9 [-16.5, 23.5, -8.7, 11.3]}

What is the slope and intercept for 2x+3y=9 2x+3y=9 and how would you graph it?