How do you graph $6x+3y=9$ by plotting points?

Question

4528 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-19T17:46:13

See a solution process below:

To graph a linear equation you just need to plot two points. First, solve for two points which solve the equation and plot these points:

First Point: For $x = 0$

$(6 * 0) + 3y = 9$

$0 + 3y = 9$

$3y = 9$

$(3y)/color(red)(3) = 9/color(red)(3)$

$y = 3$ or $(0, 3)$

Second Point: For $y = 1$

$6x + (3 * 1) = 9$

$6x + 3 = 9$

$6x + 3 - color(red)(3) = 9 - color(red)(3)$

$6x + 0 = 6$

$6x = 6$

$(6x)/color(red)(6) = 6/color(red)(6)$

$x = 1$ or $(1, 1)$

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

graph{(x^2+(y-3)^2-0.025)((x-1)^2+(y-1)^2-0.025)=0 [-10, 10, -5, 5]}

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

graph{(6x + 3y - 9)(x^2+(y-3)^2-0.025)((x-1)^2+(y-1)^2-0.025)=0 [-10, 10, -5, 5]}

How do you graph 6x+3y=96x+3y=9 by plotting points?