Graph the line with slope 3 passing through the point \( (-1,2) \)

To graph the line with a slope of 3 that passes through the point \((-1, 2)\), we can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line. In this case, \(m = 3\), \(x_1 = -1\), and \(y_1 = 2\). Substituting these values into the point-slope form, we get: \[ y - 2 = 3(x + 1) \] Now, we can simplify this equation: \[ y - 2 = 3x + 3 \] \[ y = 3x + 5 \] Now we have the equation of the line in slope-intercept form \(y = mx + b\), where \(m = 3\) and \(b = 5\). ### Steps to Graph the Line: 1. **Plot the Point**: Start by plotting the point \((-1, 2)\) on the coordinate plane. 2. **Use the Slope**: The slope of 3 means that for every 1 unit you move to the right (positive direction on the x-axis), you move up 3 units (positive direction on the y-axis). 3. **Find Another Point**: From the point \((-1, 2)\): - Move 1 unit to the right to \(x = 0\), and then move up 3 units to \(y = 5\). This gives you the point \((0, 5)\). 4. **Draw the Line**: Now that you have two points, \((-1, 2)\) and \((0, 5)\), you can draw a straight line through these points. Extend the line in both directions. 5. **Label the Line**: Optionally, you can label the line with its equation \(y = 3x + 5\). ### Summary: The line with a slope of 3 passing through the point \((-1, 2)\) can be represented by the equation \(y = 3x + 5\) and can be graphed by plotting the points \((-1, 2)\) and \((0, 5)\) and drawing a line through them.