Solve the system by graphing \( \begin{array}{l}y=\frac{1}{2} x-2 \\ y=4 x+5\end{array} \)

To solve the system by graphing, you’ll start by plotting both equations on the same coordinate plane. For the first equation, \(y = \frac{1}{2}x - 2\), identify the y-intercept at (0, -2) and then use the slope \(\frac{1}{2}\) to find another point (for example, go up 1 unit and right 2 units to (2, -1)). For the second equation, \(y = 4x + 5\), note the y-intercept at (0, 5) and a slope of 4—this means for every 1 unit you move right, you move up 4 units. After plotting these points, you’ll see where the two lines intersect; that point is the solution to the system! Remember, the intersection of the two lines gives the solution to the system of equations! If they cross at a point like (2, 3), then that means \(x = 2\) and \(y = 3\) satisfies both equations. If the lines are parallel, then there’s no solution. If they overlap, then there are infinitely many solutions! Happy graphing!