Question

Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 6x + 9y = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.

Answer 1

Step-by-step explanation

Step 1

get the slope-intercep form_

we need to use the function to graph the line,so let's convert the given equation in the slope-intercept form,to do that, isolate y

so

`\begin{gathered} -6x+9y=0 \\ \text{add 6x in both sides } \\ -6x+9y+6x=0+6x \\ 9y=6x \\ \text{divide both sides by }9 \\ (9y)/(9)=(6x)/(9) \\ y=(2)/(3)x \end{gathered}`

so, the equation of the line is

`y=(2)/(3)x`

Step 2

now, let's use the equation to find 2 coordiantes of the line

a) for x =0

`\begin{gathered} y=(2)/(3)x \\ \text{replace} \\ y=(3)/(2)(0)=0 \\ \text{hence, } \\ \text{ Point 1 ( 0,0)} \end{gathered}`

b) for x= 3

`\begin{gathered} y=(2)/(3)x \\ \text{replace} \\ y=(2)/(3)(3)=2 \\ \text{hence, } \\ \text{ Point 1 ( 3,2)} \end{gathered}`

Step 3

finally, draw a line that passes through the points (0,0) and (3,2)

I hope this helps you