The equation provided in the image is:

$y - 3x = 1$

To solve for $y$, we can rearrange this equation as follows:

1. Add $3x$ to both sides to isolate $y$: $y = 3x + 1$

This is the linear equation in slope-intercept form, $y = mx + b$, where:

• The slope ($m$) is $3$.
• The y-intercept ($b$) is $1$.

Graphing the Equation

To graph $y = 3x + 1$:

1. Start at the y-intercept, $(0, 1)$.
2. Use the slope of $3$, which means for each increase of $1$ in $x$, $y$ increases by $3$.
3. Plot additional points, such as:
   • $(0, 1)$
   • $(1, 4)$ since moving right by $1$ unit increases $y$ by $3$.
   • $(-1, -2)$ since moving left by $1$ unit decreases $y$ by $3$.

Draw a straight line through these points to complete the graph of the equation.

Would you like further details on this, or do you have any questions?

Here are related questions to expand your understanding:

1. How do you determine the slope and y-intercept from any linear equation?
2. What steps can you use to rearrange linear equations into slope-intercept form?
3. How does the slope affect the direction and steepness of the line?
4. Can you graph lines using points other than the y-intercept?
5. What does a positive slope imply about the relationship between $x$ and $y$?

Tip: When graphing, always identify the slope and intercept first; they make it easier to plot accurately.