Lydia graphed adef at the coordinates d(-2,-1), e (-2, 2), and f (0.0). she thinks adef is a right triangle. is lydia's assertion correct? yes, the slopes of ef and df are opposite reciprocals. yes, the slopes of ef and df are the same. no; the siopes of ef and df are not opposite reciprocals. no, the siopes of ef and df are not the same
check the picture below.
well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like, however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.
so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.
the direct variation says that:
then the equation is of the form is given by:
where k is the constant variation.
from the given table:
consider any value of x and m(x)=y
x = 2 and m(x)=y = 3
substitute these value in ; we have;
divide both sides by 2 we get;
put x = -1 and m(x) = -1.5
substitute in the equation:
-1.5 = -1.5 true
therefore, the function m(x) represents a direct variation
graph of this function as shown below:
english, cause i can’t you