Question

PLEASE HELP ASAP SLOPES OF PARALLEL AND PERPENDICULAR LINES

1) What is the slope of a line parallel to the line with this equation: 5x – 15y = 30
A) 1/3
B) 1/5
C) 2/3
D) 3

2) Line 1 has the equation: y = 2/3x – 5

Line 2 is parallel to Line 1.

What is the slope of Line 2?

Type your answer as a reduced fraction, like this: 3/5


3) Determine whether the pair of lines is parallel, perpendicular, or neither.
x = 2 and y = -5

A) Neither
B) perpendicular
C) Parallel


4) Determine which equation is in slope-intercept form for the line that passes through (5, 0) and is perpendicular to the line below.
y = -5/2x + 6

A) y = 5/2x + 2
B) y = 5/2x - 2
C) y = 2/5x - 2
D) y = -2/5x - 2

5) Determine the slope of the line that is perpendicular to the equation below.
y = -3x + 4
Type your answer as a reduced fraction, if necessary, like this: 3/4

Answer 1

1) Parallel lines have equal slopes.

We need to find the slope of the given line by solving for y.

5x - 15y = 30

-15y = -5x + 30

y = (1/3)x - 2

The slope of the given line is 1/3, so the slope of the parallel line is also 1/3.

2) Line 1 has slope 2/3.

Line 2 has slope 2/3.

3) Line 1 is a vertical line through x = 2. Line 2 is a horizontal line through y = -5. The lines are perpendicular.

4) The given line can is solved for y, so we can see its slope is -5/2. The slopes of perpendicular lines are negative reciprocals. The perpendicular line has slope 2/5. We have point (5, 0) which is (x1, y1) in the slope-point formula.

y - 0 = (2/5)(x - 5)

y = 2/5 x - 2

5) The given equation has slope -3. To find the negative reciprocal, write the slope as a fraction, flip it, and change the sign.

Slope of perpendicular line is 1/3.

Answer 2

The slopes of parallel lines are the same just the y-intercepts are different.

The slopes of perpendicular lines are negative reciprocals of each other.

1. -15y = -5x + 30

y = 1/3x + 2

The slope is 1/3. So, A.

2. y = 2/3x - 5

The slope is 2/3

3. x = 2 is a vertical line at x of 2

y = -5 is a horizontal line at y of -5

The two lines are perpendicular to each other. So, B.

4. y = -5/2x +6

The slope of the perpendicular line is 2/5. So, C.

5. y = -3x + 4

The slope of the perpendicular line is 1/3.

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