Answer:
y = (4/3)x -1
Explanation:
The reference line, y = -(3/4)x - 3 is in the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero). So we know the slope of this line is -(3/4). The slope of a line that is perpendicular to a reference line is the negative inverse of the reference line's slope. In this case any line with a slope of -(1/-(3/4)) is perpendicular.
We can simplify -(1/-(3/4)) to (4/3). (4/3) -s the negative inverse of -(3/4). So the new line will have the form:
y = (4/3)x + b
Any line, no matter the value of b, will be perpendicular to the reference line. But we want a line that goes through point (0,-1), so we need to make b so that the line moves through that point.
To find b that will make this happen, substitute the point (0,-1) into the unfinished equation and solve for b:
y = (4/3)x + b
-1 = (4/3)*(0) + b for point (0,-1)
b = -1
The equation of a line perpendiculat to y = -(3/4)x -3 and also goes through point (0,-1) is:
y = (4/3)x -1
See the attached graph.