The inequality that is perpendicular to y=3x+3 and passes through the points (-4,-3) and (5,3) is y + 3 < -1/3(x + 4).
To find an inequality that is perpendicular to y=3x+3 and passes through the points (-4,-3) and (5,3), we first need to determine the slope of the line y=3x+3. The equation is in the form y=mx+b, where m represents the slope. In this case, the slope is 3.
Perpendicular lines have slopes that are negative reciprocals of each other. So the slope of the line perpendicular to y=3x+3 would be -1/3. Using the point-slope form of a linear equation, we can write the equation as: y - y1 = m(x - x1). Plugging in the first point (-4,-3) and the slope -1/3, we get: y - (-3) = -1/3(x - (-4)). Simplifying, we have: y + 3 = -1/3(x + 4).
Thus, the inequality that is perpendicular to y=3x+3 and passes through the points (-4,-3) and (5,3) is y + 3 < -1/3(x + 4).
Learn more about Writing an inequality perpendicular to a given equation