# How do you graph 2x-3y+15=0?

Feb 7, 2017

Use one of 3 methods.

#### Explanation:

There are 3 methods to plot a graph from a given equation:

1. Plot points: Choose $x$-values and work out $y$-values
It is good practice to choose five $x$-values. (2 negs, 0 and 2 pos)

2. y-intercept /gradient method. Change the equation to $y = m x + c$
Plot the y-intercept and use $m = \text{rise"/"run}$ from that point.

3. -The intercept method. Find both intercepts:
To find the $x$-intercept, make $y = 0$
To find the $y$-intercept, make $x = 0$

(This does not work if the line passes through the origin.)

$2 x - 3 y + 15 = 0$

$2 x + 15 = 3 y$

$y = \frac{2}{3} x + 5$

$1$. Choose x values which are divisible by 3

$x : - 6 \text{ "-3" "0" "3" " 6" } \leftarrow$ choose
$y : + 1 \text{ "+3" "5" "7" "9" } \leftarrow$ work out

Now plot the points and join with a straight line.

$2$. $y = \frac{2}{3} x + 5$

Plot the y-intercept at 5.
Count 2 up and 3 to the right, repeat.
Count 2 down and 3 to the left, repeat.

$3$. Use $2 x - 3 y = - 15$

x-int: $2 x - 3 \left(0\right) = - 15 \text{ } \rightarrow x = - 7 \frac{1}{2}$
y-int: $2 \left(0\right) - 3 y = - 15 \text{ } \rightarrow y = 5$

Intercepts are at : $\left(- 7 \frac{1}{2} , 0\right) \mathmr{and} \left(0 , 5\right)$

The three methods will all give the graph shown:

graph{y = 2/3x+5 [-25.17, 14.83, -8.88, 11.12]}