can someone help me correct this
Directions: Dtermine which two equations represent perpendicular lines.
options are:
A) y = 2x-4
b) y = (1)/(3) x + 4
c) y= - (1)/(2)x +4
d) y = (1)/(3)x - 4
wouldn't it be a and c . Because b and d have the dame slope which are parallel lines. am i correct or wrong.
You are correct! To determine which two equations represent perpendicular lines, you need to compare their slopes. Perpendicular lines have slopes that are negative reciprocals of each other.
Let's calculate the slopes of the given options:
A) y = 2x - 4
We can rewrite this equation in slope-intercept form (y = mx + b) to find the slope. The coefficient of x (m) represents the slope in this form, so the slope of this line is 2.
B) y = (1/3)x + 4
Again, we can rewrite this equation in slope-intercept form. The coefficient of x (m) is 1/3, so the slope of this line is 1/3.
C) y = -(1/2)x + 4
Once again, rewrite the equation in slope-intercept form. Now the coefficient of x (m) is -1/2, indicating a slope of -1/2.
D) y = (1/3)x - 4
In slope-intercept form, the coefficient of x (m) is still 1/3, leading to a slope of 1/3.
Now, let's determine which pairs of equations have slopes that are negative reciprocals:
A (-1/2) and C (2) have slopes that are negative reciprocals of each other. Hence, A and C represent perpendicular lines.
Therefore, option A (y = 2x - 4) and option C (y = -(1/2)x + 4) are the correct answers for perpendicular lines.