Graph the equation. $$ x-3 y=5 $$

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UpStudy AI · Accepted Answer

Rewrite the equation by following steps:
- step0: Rewrite in slope-intercept form:
  $$x-3y=5$$
- step1: Move the expression to the right side:
  $$-3y=5-x$$
- step2: Divide both sides:
  $$y=-\frac{5}{3}+\frac{1}{3}x$$
- step3: Rearrange the terms:
  $$y=\frac{1}{3}x-\frac{5}{3}$$
To graph the equation $$ x - 3y = 5 $$, we first convert it into slope-intercept form, which is $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the y-intercept.

1. Start with the original equation:
   $$
   x - 3y = 5
   $$

2. Rearranging it to solve for $$ y $$:
   $$
   -3y = -x + 5
   $$
   $$
   y = \frac{1}{3}x - \frac{5}{3}
   $$

Now, we have the equation in slope-intercept form:
$$
y = \frac{1}{3}x - \frac{5}{3}
$$

### Key Features:
- **Slope (m)**: $$ \frac{1}{3} $$ (indicating that for every 3 units you move right, you move 1 unit up)
- **Y-intercept (b)**: $$ -\frac{5}{3} $$ (the point where the line crosses the y-axis)

### Graphing Steps:
1. Start at the y-intercept $$ (0, -\frac{5}{3}) $$.
2. From this point, use the slope to find another point. Move 3 units to the right (to $$ x = 3 $$) and 1 unit up (to $$ y = -\frac{5}{3} + 1 = -\frac{2}{3} $$), giving you the point $$ (3, -\frac{2}{3}) $$.
3. Draw a line through these points to represent the equation.

This line represents the equation $$ x - 3y = 5 $$.
To graph the equation $$ x - 3y = 5 $$, first rewrite it in slope-intercept form as $$ y = \frac{1}{3}x - \frac{5}{3} $$. Plot the y-intercept at $$ (0, -\frac{5}{3}) $$ and use the slope $$ \frac{1}{3} $$ to find another point, such as $$ (3, -\frac{2}{3}) $$. Draw a line through these points to represent the equation.

Graph the equation. \( x-3 y=5 \)

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