The point where the graphs of two linear equations intersect has a \( y \)-coordinate of 4 . One equation is \[ y=-2 x+2 \text {. Find the other equation if its graph has a slope of } 3 \text {. } \] What is the equation of the line with a slope of 3 that intersects the line with the equation \[ y=-2 x+2 \text { ? Solve on paper, and then enter your answer on Zearn. } \]

1. We are given that the graphs have an intersection point with a \( y \)-coordinate of 4. The first equation is \[ y = -2x + 2. \] Substitute \( y = 4 \) into this equation to find the \( x \)-coordinate: \[ 4 = -2x + 2. \] 2. Solve for \( x \): \[ 4 - 2 = -2x \quad \Longrightarrow \quad 2 = -2x. \] Divide both sides by \(-2\): \[ x = -1. \] So, the intersection point is \((-1, 4)\). 3. The second line has a slope of 3 and passes through the point \((-1, 4)\). Using the point-slope form: \[ y - y_1 = m(x - x_1), \] substitute \( m = 3 \), \( x_1 = -1 \), and \( y_1 = 4 \): \[ y - 4 = 3(x - (-1)) \quad \Longrightarrow \quad y - 4 = 3(x + 1). \] 4. Simplify the equation: \[ y - 4 = 3x + 3. \] Add 4 to both sides: \[ y = 3x + 7. \] The equation of the line is \( y = 3x + 7 \).