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

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Answer 1 · 2017-04-02T03:51:32

A straight line through $(0, 2)$ $(0,2)$ and $(6, 0)$ $(6,0)$

The equation of a straight line in slope $(m)$ $(m)$ and intercept $(c)$ $(c)$ form is:

$y = m x + c$ $y=mx+c$

Rewriting our equation in this form $\to y = - \frac{x}{3} + 2$ $-> y=-x/3+2$

Hence the equation is a straight line with slope $- \frac{1}{3}$ $-1/3$ and y-intercept $+ 2$ $+2$

We are asked to graph the line by plotting points.

For simplicity, I will choose the points where $x = 0$ $x=0$ and where $y = 0$ $y=0$ (NB: Any two points on this line would do)

$x = 0 \to y = 2$ $x=0 -> y=2$

$y = 0 \to - \frac{x}{3} + 2 = 0 \to x = 6$ $y=0 -> -x/3+2=0 -> x=6$

Hence the graph is a straight line through $(0, 2)$ $(0,2)$ and $(6, 0)$ $(6,0)$ as shown below:

graph{-x/3+2 [-2.446, 10.04, -2.695, 3.55]}

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