**Graphing Linear Equations: Example 1** In this exercise, we are tasked with graphing the linear equation: \[ 5x + y = 5 \] ### Steps to Graph the Equation 1. **Convert to Slope-Intercept Form:** The equation can be rewritten in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. \[ 5x + y = 5 \] \[ y = -5x + 5 \] Here, the slope \( m \) is \(-5\) and the y-intercept \( b \) is \(5\). 2. **Identify Key Points:** - **Y-Intercept:** The y-intercept is the point where the line crosses the y-axis (\(y = 5\)). - **X-Intercept:** Set \( y = 0 \) and solve for \( x \): \[ 0 = -5x + 5 \] \[ 5x = 5 \] \[ x = 1 \] So, the x-intercept is at \( (1, 0) \). 3. **Plot the Points:** - Plot the y-intercept (0, 5) on the graph. - Plot the x-intercept (1, 0) on the graph. 4. **Draw the Line:** Connect these points with a straight line extending across the grid. This line represents the equation \( y = -5x + 5 \). ### Description of the Graph The graph is drawn on a Cartesian coordinate system with both x and y axes ranging from -20 to 20. The graph should ideally show a straight line passing through the points (0, 5) and (1, 0), sloping downwards from left to right. This exercise helps visualize how linear equations create straight lines, using intercepts and slopes to determine the line's position and direction on the graph. **Title: Understanding Intercepts in Graphs** **Part 2 of 2** In this section, you are tasked with identifying the x-intercepts and y-intercepts of a given graph. Each intercept should be written as an ordered pair. - **x-intercept(s):** [ ] - Input format: ( , ) - **y-intercept(s):** [ ] - Input format: ( , ) A graphical interface allows you to enter intercepts, featuring boxes for user input and a cursor. A "Start Over" button is provided to clear entries and restart the task. --- **How to Find Intercepts:** - **x-intercept:** The point(s) where the graph crosses the x-axis. Here, y = 0. - **y-intercept:** The point(s) where the graph crosses the y-axis. Here, x = 0. Ensure that each intercept is accurately recorded as an ordered pair (x, y). For further assistance or a step-by-step guide, feel free to reach out to your instructor or consult additional resources.