Question

Use the image to answer the question.

A coordinate graph shows both the x and y axes ranging from negative 5 to 5 in unit increments. Four lines are plotted.

Image Long DescriptionLine upper A is a small dash-dot-small dash line labeled as y equals negative 5 times x plus 3. It passes through left parenthesis 0 comma 3 right parenthesis and left parenthesis 1 comma negative 2 right parenthesis. Line upper B is a large dash-dot-large dash line labeled as y equals negative start fraction 1 over 6 end fraction times x minus 1. It passes through left parenthesis 0 comma negative 1 right parenthesis and approximately left parenthesis 5 comma negative 1.9 right parenthesis. Line upper C is a dotted line labeled as y equals 5 times x plus 2. It passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis negative 1 comma negative 3 right parenthesis. Line upper D is a solid line labeled as y equals start fraction 1 over 5 end fraction times x minus 2. It passes through left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 5 comma negative 1 right parenthesis. All lines have arrows at both ends.

Lines A, B, C, and D are graphed and labeled. Based on their slopes, which two lines are perpendicular?

(1 point)
Responses

Line A
is perpendicular to line C
.
Line upper A is perpendicular to line upper C .

Line C
is perpendicular to line D
.
Line upper C is perpendicular to line upper D .

Line B
is perpendicular to line C
.
Line upper B is perpendicular to line upper C .

Line A
is perpendicular to line D
.
Line upper A is perpendicular to line upper D .

Answer 1

To determine which two lines are perpendicular, we need to look at the slopes of each line as the product of the slopes of two perpendicular lines is -1.

1. **Line A**: \( y = -5x + 3 \) has a slope of -5.

2. **Line B**: \( y = -\frac{1}{6}x - 1 \) has a slope of -\(\frac{1}{6}\).

3. **Line C**: \( y = 5x + 2 \) has a slope of 5.

4. **Line D**: \( y = \frac{1}{5}x - 2 \) has a slope of \(\frac{1}{5}\).

Now we multiply the slopes of the pairs to check for perpendicularity:

- **Line A and Line C**: \(-5 \cdot 5 = -25\) (not perpendicular)
- **Line A and Line D**: \(-5 \cdot \frac{1}{5} = -1\) (perpendicular)
- **Line B and Line C**: \(-\frac{1}{6} \cdot 5 = -\frac{5}{6}\) (not perpendicular)
- **Line B and Line D**: \(-\frac{1}{6} \cdot \frac{1}{5} = -\frac{1}{30}\) (not perpendicular)

So, the lines that are perpendicular are:

**Line A is perpendicular to Line D.**