Solve this system of equations by graphing. First graph the equations, and then type the solution. \[ y=\frac{5}{2} x+1 \] \( x=-2 \) Click to select points on the graph.

To solve the system of equations by graphing, let's analyze each equation: 1. **First Equation:** \( y = \frac{5}{2}x + 1 \) - This is a linear equation in slope-intercept form (\( y = mx + b \)) where: - **Slope (m):** \( \frac{5}{2} \) - **Y-intercept (b):** \( 1 \) - **Graphing the First Equation:** - Start by plotting the y-intercept at \( (0, 1) \). - From the y-intercept, use the slope to find another point. Since the slope is \( \frac{5}{2} \), you can go up 5 units and right 2 units to reach the next point at \( (2, 6) \). - Draw a straight line through these points. 2. **Second Equation:** \( x = -2 \) - This is a vertical line where all points on the line have an x-coordinate of \( -2 \). - **Graphing the Second Equation:** - Draw a vertical line that crosses the x-axis at \( x = -2 \). 3. **Finding the Intersection:** - The solution to the system is the point where the two graphs intersect. - To find this, substitute \( x = -2 \) into the first equation to find the corresponding y-value: \[ y = \frac{5}{2}(-2) + 1 = -5 + 1 = -4 \] - So, the point of intersection is \( (-2, -4) \). **Solution:** \( (-2,\, -4) \)