First convert the equation to slop intercept form:
2x - 7y - 21 = 0
7y = -2x + 21
y = -2/7x + 3
the equation of the perpendicular will always have a slope that is the negative reciprocal of the original slope.
- the perpendicular line's slope will be 7/2
The question says it has the same y-intercept, (0, 3), so the final equation will be y = 7/2x + 3
The attached image is a graph of the two lines. Sure enough, they're perpendicular with the same y-intercept.
