Graph the line that passes through 24. \( (-3,-2) ; m=2 \)

To graph the line that passes through the point \((-3, -2)\) with a slope \(m = 2\), 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 \((x_1, y_1)\) is a point on the line and \(m\) is the slope. ### Step 1: Substitute the known values Here, \((x_1, y_1) = (-3, -2)\) and \(m = 2\). Substituting these values into the equation gives: \[ y - (-2) = 2(x - (-3)) \] This simplifies to: \[ y + 2 = 2(x + 3) \] ### Step 2: Simplify the equation Now, we can simplify this equation: \[ y + 2 = 2x + 6 \] Subtracting 2 from both sides: \[ y = 2x + 4 \] ### Step 3: Graph the line To graph the line \(y = 2x + 4\): 1. **Identify the y-intercept**: The y-intercept is \(4\) (where the line crosses the y-axis). 2. **Use the slope**: The slope \(2\) means that for every 1 unit you move to the right (positive x-direction), you move up 2 units (positive y-direction). ### Step 4: Plot points - Start at the y-intercept \((0, 4)\). - From there, move right 1 unit to \(x = 1\) and up 2 units to \(y = 6\), giving the point \((1, 6)\). - You can also go left from the y-intercept: move left 1 unit to \(x = -1\) and down 2 units to \(y = 2\), giving the point \((-1, 2)\). ### Final Graph You can now draw a straight line through the points \((-3, -2)\), \((0, 4)\), and \((1, 6)\) to represent the line \(y = 2x + 4\). If you have graphing software or graph paper, you can plot these points and draw the line accordingly.