\( \leftarrow \begin{array}{l}\text { Graph the linear equation. } \\ 4 x+2 y=16\end{array} \)

Rewrite the equation by following steps: - step0: Rewrite in slope-intercept form: \(4x+2y=16\) - step1: Move the expression to the right side: \(2y=16-4x\) - step2: Divide both sides: \(y=8-2x\) - step3: Rearrange the terms: \(y=-2x+8\) To graph the linear equation \(4x + 2y = 16\), we first convert it to slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. 1. **Convert to Slope-Intercept Form:** \[ 4x + 2y = 16 \] Subtract \(4x\) from both sides: \[ 2y = -4x + 16 \] Now, divide by \(2\): \[ y = -2x + 8 \] Here, the slope \(m = -2\) and the y-intercept \(b = 8\). 2. **Identify Key Points:** - The y-intercept is at the point \((0, 8)\). - To find another point, we can choose \(x = 2\): \[ y = -2(2) + 8 = 4 \quad \text{(Point: (2, 4))} \] - Another point can be found by choosing \(x = 4\): \[ y = -2(4) + 8 = 0 \quad \text{(Point: (4, 0))} \] 3. **Plotting the Points:** - Plot the points \((0, 8)\), \((2, 4)\), and \((4, 0)\) on a graph. - Draw a straight line through these points to represent the equation. The graph of the equation \(4x + 2y = 16\) is a straight line with a slope of \(-2\) and a y-intercept of \(8\).