Use the following lines to answer the question.
line g: y=−4/5x+7/5
line h: y=5/4x+3/4
Is line g perpendicular to line h? Why or why not?
A. Yes, because the slopes of lines g and h are opposite and the y-intercepts are different.
B. Yes, because the slopes of lines g and h are opposite and reciprocal.
C. No, because the y-intercepts of lines g and h are different.
D. No, because the slopes of lines g and h have different signs.
I believe the answer is C
Perpendicular has to do with the slopes.
The slopes are connected to the x variables.
Check the slopes...
Do they multiply to -1??
If yes, then the lines are perpendicular : )
So... C is NOT the correct answer...
I line G as -20 and line H as 20
So does that mean the answer is B because they are opposite?
Yes, -20/20
that is -20 divided by 20, which is -1
Thus the lines have negative reciprocals... then thus perpendicular : )
(-4/5)x(5/4) = (-20)/20
= -1 : )
To determine if line g is perpendicular to line h, we need to compare their slopes.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
For line g: y = -4/5x + 7/5, the slope is -4/5.
For line h: y = 5/4x + 3/4, the slope is 5/4.
To check if lines g and h are perpendicular, we can compare their slopes.
If two lines are perpendicular, their slopes must be negative reciprocals of each other. The negative reciprocal of a number is the negative value of its reciprocal.
The reciprocal of -4/5 is -5/4.
Comparing the slopes of lines g and h, we see that -4/5 and -5/4 are indeed negative reciprocals of each other.
Therefore, the correct answer is B. Yes, because the slopes of lines g and h are opposite and reciprocal.