To graph a line with the given features, y-intercept = 1 and slope = -2/3, follow these steps:

Step-by-Step Instructions:

1. Start at the y-intercept: The y-intercept is the point where the line crosses the y-axis. For this line, the point is $(0, 1)$.

2. Use the slope to find another point: The slope is $-\frac{2}{3}$. This means that for every 3 units you move to the right, the line goes down 2 units.

   • From $(0, 1)$, move 3 units to the right (x = 3), and then 2 units down (y = -1). This gives another point: $(3, -1)$.

3. Plot these points: Plot $(0, 1)$ and $(3, -1)$ on the graph.

4. Draw the line: Use a ruler to draw a straight line through the points.

Equation of the Line:

The slope-intercept form of a line is: $y = mx + b$ Where:

• $m$ is the slope ($-2/3$),
• $b$ is the y-intercept (1).

Thus, the equation is: $y = -\frac{2}{3}x + 1$

Would you like a graph of this line? Let me know! 😊

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Related Questions:

1. How can the slope of a line determine its steepness and direction?
2. What happens if the slope is positive instead of negative?
3. How can we convert this line into standard form ($Ax + By = C$)?
4. What are parallel and perpendicular slopes to this line?
5. How would the graph change if the y-intercept were at $y = 2$?

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Tip:

The slope tells you how steep the line is and whether it ascends ($m > 0$) or descends ($m < 0$) as you move left to right.