To solve this, let’s analyze the equation $3x + y = 1$ and determine the slope and y-intercept.

Step 1: Rewrite the equation in slope-intercept form ($y = mx + b$)

We start with: $3x + y = 1$ Subtract $3x$ from both sides: $y = -3x + 1$

Step 2: Identify the slope and y-intercept

From the equation $y = mx + b$:

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

Step 3: Graphing the line

To graph the line:

1. Plot the y-intercept point $(0, 1)$ on the y-axis.
2. Use the slope $-3$, which means "down 3 units and right 1 unit," to find another point. Starting at $(0, 1)$, move down 3 units to $-2$ and right 1 unit to $1$. This gives the second point $(1, -2)$.
3. Draw a straight line through these two points.

Would you like a visual graph or further details on this?

Related Questions

1. How do you find the x-intercept of the equation $3x + y = 1$?
2. What is the significance of the slope in a graph?
3. Can you write the equation in standard form again after graphing it?
4. What happens to the graph if the slope becomes $-1$ instead of $-3$?
5. How do you check if a point lies on the line $3x + y = 1$?

Tip

Always simplify equations into slope-intercept form ($y = mx + b$) when finding the slope and intercept for easier graphing.