Graph the line with the equation \( y=-\frac{1}{5} x-3 \)

Sure! Let's graph the linear equation \( y = -\frac{1}{5}x - 3 \). ### 1. Understanding the Equation The equation is 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). For \( y = -\frac{1}{5}x - 3 \): - **Slope (m)** = -\(\frac{1}{5}\) - **Y-intercept (b)** = -3 ### 2. Plotting the Graph #### Step 1: Plot the Y-intercept Start by plotting the y-intercept (\(0, -3\)) on the graph. #### Step 2: Use the Slope to Find Another Point The slope \( -\frac{1}{5} \) means that for every 5 units you move to the right (positive direction on the x-axis), you move down by 1 unit (negative direction on the y-axis). From the y-intercept (\(0, -3\)): - Move 5 units to the right: \( x = 0 + 5 = 5 \) - Move 1 unit down: \( y = -3 - 1 = -4 \) - Plot the point (\(5, -4\)) Alternatively, you can move 5 units to the left and 1 unit up: - Move 5 units to the left: \( x = 0 - 5 = -5 \) - Move 1 unit up: \( y = -3 + 1 = -2 \) - Plot the point (\(-5, -2\)) #### Step 3: Draw the Line Connect the plotted points with a straight line extending in both directions. ### 3. Visual Representation Here's a simple graph illustrating the line: ``` y | | * | (5,-4) | | |* (-5,-2) |(0,-3) |________________________ x ``` - The point **(0, -3)** is the y-intercept. - The point **(5, -4)** is obtained using the slope. - The point **(-5, -2)** is another point on the line using the slope in the opposite direction. ### 4. Summary - **Y-intercept**: (0, -3) - **Slope**: -1/5 (down 1 unit for every 5 units to the right) - **Another Point**: (5, -4) or (-5, -2) By plotting these points and drawing a line through them, you get the graph of the equation \( y = -\frac{1}{5}x - 3 \). If you have graphing software or a graphing calculator, you can input the equation to see a more precise graph. Let me know if you need further assistance!