Question

How do you graph `3x + 5y = 6` by plotting points?

Answer 1

See a solution process below:

Explanation:

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

First Point: For `y = 0`

`3x + (5 * 0) = 6`

`3x + 0 = 6`

`3x = 6`

`(3x)/color(red)(3) = 6/color(red)(3)`

`x = 2` or `(2, 0)`

Second Point: For `y = 3`

`3x + (5 * 3) = 6`

`3x + 15 = 6`

`3x + 15 - color(red)(15) = 6 - color(red)(15)`

`3x + 0 = -9`

`3x = -9`

`(3x)/color(red)(3) = -9/color(red)(3)`

`x = -3` or `(-3, 3)`

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

graph{((x-2)^2+y^2-0.035)((x+3)^2+(y-3)^2-0.035)=0 [-10, 10, -5, 5]}

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

graph{(3x+5y-6)((x-2)^2+y^2-0.035)((x+3)^2+(y-3)^2-0.035)=0 [-10, 10, -5, 5]}