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:

Let's analyze and graph the given linear equations, identify their forms, and determine their solutions. ### Given Equations: 1. \( y = 4x + 4 \) 2. \( y = -12 \) ### Step 1: Write Both Equations in Slope-Intercept Form The slope-intercept form of a linear equation is: \[ y = mx + b \] where: - \( m \) is the slope, - \( b \) is the y-intercept. **First Equation:** \[ y = 4x + 4 \] This equation is already in slope-intercept form. - **Slope (\( m \))**: 4 - **Y-intercept (\( b \))**: 4 **Second Equation:** \[ y = -12 \] To express this in slope-intercept form, recognize that it is a horizontal line where the slope is 0. \[ y = 0x - 12 \] - **Slope (\( m \))**: 0 - **Y-intercept (\( b \))**: -12 ### Step 2: Graphing the Equations 1. **Graph of \( y = 4x + 4 \):** - **Slope (4):** For every 1 unit increase in \( x \), \( y \) increases by 4 units. - **Y-intercept (4):** The line crosses the y-axis at (0, 4). 2. **Graph of \( y = -12 \):** - This is a horizontal line that crosses the y-axis at (0, -12). *Graph Illustration:* ``` y | | / | / | / y = 4x + 4 |-------/--------x | / | / | / y = -12 | ``` ### Step 3: Identifying the Number of Solutions To find the solution(s) where the two lines intersect, we set the equations equal to each other: \[ 4x + 4 = -12 \] **Solving for \( x \):** \[ \begin{align*} 4x + 4 &= -12 \\ 4x &= -12 - 4 \\ 4x &= -16 \\ x &= -4 \end{align*} \] **Finding \( y \):** Plugging \( x = -4 \) into either equation (using \( y = -12 \) is simplest): \[ y = -12 \] **Solution Point:** \[ (-4, -12) \] ### Summary - **Slope-Intercept Forms:** \[ \begin{align*} y &= 4x + 4 \\ y &= 0x - 12 \end{align*} \] - **Number of Solutions:** - **One solution** - **Point of Intersection:** \[ (-4, -12) \] This means the two lines intersect at exactly one point, which is \((-4, -12)\).