Select the TWO lines from this list that are perpendicular.
Responses
4x−3y=−6
4 x minus 3 y is equal to negative 6
y−2=34(x+1)
y minus 2 is equal to 3 fourths times open paren x plus 1 close paren
y=−34x+12
y is equal to negative 3 fourths x plus 12
5x−3y=−3
To determine whether two lines are perpendicular, we need to look at the slopes of the lines. If the product of the slopes of two lines is -1, then the lines are perpendicular.
Let's first write each equation in slope-intercept form (y = mx + b), where m is the slope of the line.
1. 4x − 3y = −6
To find the slope, isolate y:
-3y = -4x - 6
y = (4/3)x + 2
The slope of this line (m1) is 4/3.
2. y − 2 = 3/4(x + 1)
Expand the right side:
y = 3/4x + 3/4 + 2
y = 3/4x + 11/4
The slope of this line (m2) is 3/4.
3. y = −3/4x + 12
The slope of this line (m3) is -3/4.
4. 5x − 3y = −3
Isolate y:
-3y = -5x - 3
y = (5/3)x + 1
The slope of this line (m4) is 5/3.
Now that we have the slopes, let's find the products of the pairs:
m1 * m3 = (4/3) * (-3/4) = -1
m2 * m4 = (3/4) * (5/3) ≠ -1 (The product is 5/4, which isn't -1)
The only pair of slopes that has a product of -1 is m1 and m3, which are the slopes for the first equation (4x − 3y = −6) and the third equation (y = −3/4x + 12). Therefore, the lines represented by these two equations are perpendicular to each other.