Final answer:
The equation of a line that passes through the point (2, −10) and is parallel to 14x + 2y = 6 is y = -7x + 4.
Step-by-step explanation:
The equation of a line that is parallel to another line can be found using the same slope as the given line. Since the given line has the equation 14x + 2y = 6, we need to rearrange it to solve for y. This gives us the equation y = -7x + 3. The slope of this line is -7, so the parallel line will also have a slope of -7. We can plug in the point (2, -10) into the slope-intercept form of a line, y = mx + b, to find the value of b. Substituting the values, we get -10 = -7(2) + b. Solving for b gives us b = -10 + 14 = 4. Therefore, the equation of the line that passes through the point (2, -10) and is parallel to 14x + 2y = 6 is y = -7x + 4.