Question

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

Answer 1

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 = mx+c`
   Plot the y-intercept and use `m = "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.)

`2x-3y+15 =0`

`2x+15 = 3y`

`y = 2/3x+5`

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

`x: -6" "-3" "0" "3" " 6" "larr` choose
`y: +1" "+3" "5" "7" "9" "larr` work out

Now plot the points and join with a straight line.

`2`. `y = 2/3x+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 `2x -3y = -15`

x-int: `2x - 3(0) = -15 " " rarr x = -7 1/2`
y-int: `2(0) -3y =-15" "rarr y = 5`

Intercepts are at : `(-7 1/2, 0) and (0,5)`

The three methods will all give the graph shown:

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