Question

How do you graph `9x+2y=5`?

Answer 1

See a solution process below:

Explanation:

First, solve for two points which solve the equation and plot these points:

First Point: For `x = 1`

`(9 * 1) + 2y = 5`

`9 + 2y = 5`

`-color(red)(9) + 9 + 2y = -color(red)(9) + 5`

`0 + 2y = -4`

`2y = -4`

`(2y)/color(red)(2) = -4/color(red)(2)`

`y = -2` or `(1, -2)`

Second Point: For `x = -1`

`(9 * -1) + 2y = 5`

`-9 + 2y = 5`

`color(red)(9) - 9 + 2y = color(red)(9) + 5`

`0 + 2y = 14`

`2y = 14`

`(2y)/color(red)(2) = 14/color(red)(2)`

`y = 7` or `(-1, 7)`

We can next plot the two points on the coordinate plane:

graph{((x-1)^2+(y+2)^2-0.125)((x+1)^2+(y-7)^2-0.125)=0 [-20, 20, -10, 10]}

Now, we can draw a straight line through the two points to graph the line:

graph{(9x+2y-5)((x-1)^2+(y+2)^2-0.125)((x+1)^2+(y-7)^2-0.125)=0 [-20, 20, -10, 10]}