Answer \[ y=4 x+4 y=-12 \] Graph the linear equations by writing the equations in slope-intercept form: \[ y=\square x+\square+\square \] Identify the appropriate number of solutions. If there is a solution, give the point:

To graph the equations, we first need to convert both equations into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Starting with the first equation: 1. \(y = 4x + 4\) is already in slope-intercept form with a slope of \(4\) and a y-intercept of \(4\). Now for the second equation: 2. Rearranging \(4y = -12\) gives us: \[ y = -3 \] This indicates that the second equation is a horizontal line at \(y = -3\). Now, let's analyze them together: - The first equation, \(y = 4x + 4\), is a line that rises steeply. - The second equation represents a line parallel to the x-axis. To find the point of intersection, we set the two equations equal to each other: \[ 4x + 4 = -3 \] Solving for \(x\): \[ 4x = -3 - 4 \] \[ 4x = -7 \] \[ x = -\frac{7}{4} \] Substituting \(x = -\frac{7}{4}\) back into the first equation to find \(y\): \[ y = 4\left(-\frac{7}{4}\right) + 4 = -7 + 4 = -3 \] So the point of intersection, which is our solution, is: \[ \left(-\frac{7}{4}, -3\right) \] The equations intersect at one point, confirming there is exactly one solution.