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 \[ y=-2 x+2 \text { ? Solve on paper, and then enter your answer on Zearn. } \]

To find the equation of the line with a slope of 3 that intersects \( y = -2x + 2 \) at a \( y \)-coordinate of 4, we start by using the point-slope form of a linear equation, which is written as: \[ y - y_1 = m (x - x_1) \] Given that the slope \( m \) is 3, and the intersecting point has coordinates \( (x, 4) \), we can derive \( x \) from the first equation at \( y = 4 \): Setting \( y = 4 \) in \( y = -2x + 2 \): \[ 4 = -2x + 2 \] Solving for \( x \): \[ 4 - 2 = -2x \] \[ 2 = -2x \] \[ x = -1 \] Now, we know the intersection point is \( (-1, 4) \). Let's use this point in the point-slope form equation: \[ y - 4 = 3(x + 1) \] Expanding and simplifying it: \[ y - 4 = 3x + 3 \] \[ y = 3x + 7 \] So the other equation is: \[ y = 3x + 7 \]