Ease Into Prep with an SAT^® Question of the Day

Recall that the slopes of perpendicular lines are negative (or opposite) reciprocals. Use this information to find the slope of line l. Then plug in the point (2, 3) to find its y-intercept.

Begin by rewriting 2x + 5y = −7 in slope-intercept form, y = mx + b:
2x + 5y = −7
5y = −2x-7
y= −(2/5)x −7/5
The slope of this line is −2/5. Since line l is perpendicular, it has a negative reciprocal slope. Thus, the slope of line l is 5/2. Begin constructing the equation for line l:
y = 5/2x + b
You are given that line l passes through the point (2, 3). Plug in this point and solve for b:
3 = (5/2)(2) + b
3 = 5 + b
-2 = b
Thus, the y-intercept of line l is −2. Choice (D) is correct.