Determine which two equations represent perpendicular lines.
(a) y = 3/10x -3
(b) y= - 10/3x -3
(c) y = -1/5x + 3/10
(d) y = 1/5x – 3/10
Equations (a) and (b) are perpendicular t one another, because the product of the slopes is -1.
To determine if two lines are perpendicular, you need to check if the product of their slopes is -1.
Let's calculate the slopes of the given equations to find the perpendicular lines:
(a) The slope of equation (a) is 3/10.
(b) The slope of equation (b) is -10/3.
(c) The slope of equation (c) is -1/5.
(d) The slope of equation (d) is 1/5.
Now, let's check the product of the slopes of each pair of equations:
(a) * (b) = (3/10) * (-10/3) = -1
The product of the slopes of equations (a) and (b) is -1, which means they are perpendicular to each other.
Therefore, equations (a) and (b) represent perpendicular lines.