Question
Write an equation in slope-intercept form for the line whose slope is equal to 2 1 and whose y-intercept is equal to -6. Then, graph the line. Equation: □
Answers
GPT-4o mini
To write the equation of a line in slope-intercept form, we use the formula:
\[ y = mx + b \]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept.
Given:
- Slope \( m = 2 \),
- Y-intercept \( b = -6 \).
Plugging these values into the equation gives us:
\[ y = 2x - 6 \]
Now, let's graph the line defined by this equation:
1. Start at the y-intercept (0, -6) on the y-axis.
2. From that point, use the slope to find another point. The slope of 2 can be written as \(\frac{2}{1}\), meaning rise (y) of 2 and run (x) of 1.
3. From (0, -6), move up 2 units (to -4) and 1 unit to the right (to 1). This gives the point (1, -4).
4. You can add more points by repeating the slope. From (1, -4), move up 2 again and 1 to the right to get (2, -2).
5. Alternatively, you can also go backwards. From (0, -6), move down 2 units (to -8) and 1 unit to the left (to -1) to get (-1, -8).
**Graphing Steps:**
- Plot the points (0, -6), (1, -4), and (2, -2) on a graph.
- Draw a straight line through these points, extending it in both directions.
The equation of the line is:
\[ \boxed{y = 2x - 6} \]
\[ y = mx + b \]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept.
Given:
- Slope \( m = 2 \),
- Y-intercept \( b = -6 \).
Plugging these values into the equation gives us:
\[ y = 2x - 6 \]
Now, let's graph the line defined by this equation:
1. Start at the y-intercept (0, -6) on the y-axis.
2. From that point, use the slope to find another point. The slope of 2 can be written as \(\frac{2}{1}\), meaning rise (y) of 2 and run (x) of 1.
3. From (0, -6), move up 2 units (to -4) and 1 unit to the right (to 1). This gives the point (1, -4).
4. You can add more points by repeating the slope. From (1, -4), move up 2 again and 1 to the right to get (2, -2).
5. Alternatively, you can also go backwards. From (0, -6), move down 2 units (to -8) and 1 unit to the left (to -1) to get (-1, -8).
**Graphing Steps:**
- Plot the points (0, -6), (1, -4), and (2, -2) on a graph.
- Draw a straight line through these points, extending it in both directions.
The equation of the line is:
\[ \boxed{y = 2x - 6} \]