Question

Which line is parallel to the line y=−32x−5
and goes through the point (0,2)
?(1 point)
Responses

y=−32x+2
y equals negative Start Fraction 3 over 2 End Fraction x plus 2

y=−32(x+103)
y equals negative Start Fraction 3 over 2 End Fraction open parenthesis x plus start fraction 10 over 3 end fraction close parenthesis

y=−32x
y equals negative Start Fraction 3 over 2 End Fraction x

3y=−2x−15

Answer 1

To find a line that is parallel to the line given by the equation \( y = -32x - 5 \) and passes through the point \( (0, 2) \), we need to remember that parallel lines have the same slope.

1. The slope of the given line \( y = -32x - 5 \) is \( -32 \).
2. A parallel line will also have a slope of \( -32 \).

Now, we can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope.

Given the point \( (0, 2) \), we can plug in the values:

- \( x_1 = 0 \)
- \( y_1 = 2 \)
- \( m = -32 \)

Substituting these into the point-slope formula, we get:

\[
y - 2 = -32(x - 0)
\]

Simplifying this:

\[
y - 2 = -32x
\]

\[
y = -32x + 2
\]

Thus, the equation of the line that is parallel to the given line and passes through the point \( (0, 2) \) is:

\[
y = -32x + 2
\]

From the provided options:

- **y = -32x + 2** (correct answer)

Therefore, the correct response is:

**y = -32x + 2**