To determine equations that are parallel or perpendicular to a given equation, we need to consider the slope of the given equation.
The equation 6x - 2y = -7 can be rewritten in slope-intercept form as:
y = 3x + 7/2
where the slope is 3.
To find an equation that is parallel to the given equation, we can use the same slope of 3. An example of a parallel equation is:
y = 3x + 2
To find an equation that is perpendicular to the given equation, we need to use a slope that is the negative reciprocal of the slope of the given equation. The negative reciprocal of 3 is -1/3. An example of a perpendicular equation is:
y = (-1/3)x + 4