Final answer:
To find an equation for the line parallel to 2y + 12x = 14 and goes through the point (-10, 7), you can use the point-slope form with the given slope and point.
Step-by-step explanation:
To find an equation for the line parallel to 2y + 12x = 14 and goes through the point (-10, 7), we need to determine the slope of the given line and then use that slope to find the equation of the parallel line.
First, we need to rewrite the given equation 2y + 12x = 14 in slope-intercept form (y = mx + b) by isolating y. Subtract 12x from both sides of the equation:
2y = -12x + 14
Divide both sides by 2 to solve for y:
y = -6x + 7
Since the parallel line will have the same slope as the given line, the slope of the parallel line is -6. Now we can use the point-slope form (y - y1 = m(x - x1)) with the slope -6 and the point (-10, 7) to find the equation of the parallel line. Plug in the values:
y - 7 = -6(x - (-10))
Simplify: y - 7 = -6(x + 10)
Expand the equation: y - 7 = -6x - 60
Move the constant term to the other side of the equation: y = -6x - 60 + 7
Simplify: y = -6x - 53
Therefore, the equation for the line parallel to 2y + 12x = 14 and goes through the point (-10, 7) is y = -6x - 53.