Graph this line: \[ y+1=-3(x+1) \] Click to select points on the graph.

Sure! Let's graph the line defined by the equation: \[ y + 1 = -3(x + 1) \] ### Step 1: Rewrite the Equation in Slope-Intercept Form First, let's rewrite the equation in the slope-intercept form \( y = mx + b \), where: - \( m \) is the slope of the line. - \( b \) is the y-intercept (the point where the line crosses the y-axis). Starting with: \[ y + 1 = -3(x + 1) \] Distribute the \(-3\) on the right side: \[ y + 1 = -3x - 3 \] Subtract 1 from both sides to solve for \( y \): \[ y = -3x - 4 \] Now, the equation is in slope-intercept form: \[ y = -3x - 4 \] ### Step 2: Identify the Slope and Y-Intercept - **Slope (\( m \))**: \(-3\) - **Y-intercept (\( b \))**: \(-4\) This means the line crosses the y-axis at \((0, -4)\) and has a slope of \(-3\), indicating it goes down 3 units for every 1 unit it moves to the right. ### Step 3: Plot the Y-Intercept Start by plotting the y-intercept on the graph: - **Point 1**: \((0, -4)\) ### Step 4: Use the Slope to Find Another Point From the y-intercept \((0, -4)\), use the slope \(-3\) to find the next point: - **Slope** of \(-3\) means "rise over run" is \(-3/1\). - Starting at \((0, -4)\), move **down 3 units** and **right 1 unit** to reach the next point. - **Point 2**: \((1, -7)\) ### Step 5: Plot Additional Points (Optional) To make the graph more accurate, plot additional points: - **Point 3**: Choose \( x = -1 \) \[ y = -3(-1) - 4 = 3 - 4 = -1 \] So, \((-1, -1)\) - **Point 4**: Choose \( x = 2 \) \[ y = -3(2) - 4 = -6 - 4 = -10 \] So, \((2, -10)\) ### Step 6: Draw the Line Once you've plotted at least two points, draw a straight line through them. Continue the line in both directions, adding arrows to indicate it extends infinitely. ### Summary of Points to Plot | \( x \) | \( y \) | |---------|----------| | -1 | -1 | | 0 | -4 | | 1 | -7 | | 2 | -10 | ### Visual Representation While I can't create interactive graphs here, you can use graphing tools like [Desmos](https://www.desmos.com/calculator) or graph paper to plot the points and draw the line. **Graph Description:** - The line crosses the y-axis at \((0, -4)\). - It slopes downward steeply due to the slope of \(-3\). - Points like \((-1, -1)\), \((1, -7)\), and \((2, -10)\) lie on the line. Here's a simple sketch of what the graph would look like: ``` y | | * | * | * | * | * | * |--------------------------- x ``` *(Each "*" represents a plotted point along the line.)* ### Interactive Graphing Tools For an interactive experience where you can click to select points, consider using online graphing calculators such as: - **Desmos:** [https://www.desmos.com/calculator](https://www.desmos.com/calculator) - **GeoGebra:** [https://www.geogebra.org/graphing](https://www.geogebra.org/graphing) These tools allow you to input the equation and visualize the graph dynamically. --- If you have access to a specific graphing tool or need further assistance with plotting points, feel free to ask!