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

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Answer 1 · 2018-04-07T15:36:02

See a solution process below:

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

First Point: For $y = 0$ $y = 0$

$3 x + (5 \cdot 0) = 6$ $3x + (5 * 0) = 6$

$3 x + 0 = 6$ $3x + 0 = 6$

$3 x = 6$ $3x = 6$

$\frac{3 x}{3} = \frac{6}{3}$ $(3x)/color(red)(3) = 6/color(red)(3)$

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

Second Point: For $y = 3$ $y = 3$

$3 x + (5 \cdot 3) = 6$ $3x + (5 * 3) = 6$

$3 x + 15 = 6$ $3x + 15 = 6$

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

$3 x + 0 = - 9$ $3x + 0 = -9$

$3 x = - 9$ $3x = -9$

$\frac{3 x}{3} = - \frac{9}{3}$ $(3x)/color(red)(3) = -9/color(red)(3)$

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

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]}

How do you graph 3x + 5y = 63x+5y=63x + 5y = 6 by plotting points?