Final answer:
To find the equation of the line parallel to the given line and passing through the given point, we can determine the slope of the given line, use the point-slope form of a linear equation, and substitute the coordinates of the point into the equation. The equation of the parallel line is y = -2x + 8. To find the y-coordinate of the point on this line with x = 12.6, we can substitute the x-value into the equation and solve for y.
Step-by-step explanation:
To find the equation of the line parallel to the line 2y + 4x = 7, we need to determine the slope of the given line and use the point-slope form of a linear equation. The given line can be rewritten in slope-intercept form as y = -2x + 7/2. The slope of this line is -2. Since the parallel line has the same slope, its equation can be written as y = -2x + b, where we need to determine the value of b. We are given that the parallel line passes through the point (5, -2). Substituting the coordinates of this point into the equation gives -2 = -2(5) + b. Solving for b, we get b = 8. Therefore, the equation of the parallel line is y = -2x + 8.
To find the y-coordinate of the point on this line with x = 12.6, we can substitute this x-value into the equation and solve for y. Plugging in x = 12.6, we have y = -2(12.6) + 8. Simplifying the expression gives y = -25.2 + 8, which equals -17.2. Therefore, the y-coordinate of the point on the line with x = 12.6 is -17.2.