Question

Which line is perpendicular to the line y=5x−2
and goes through the point (2,3)
?(1 point)
Responses

y+3=15(x−2)
y plus 3 equals Start Fraction 1 over 5 End Fraction left parenthesis x minus 2 right parenthesis

y−3=5(x−2)
y minus 3 equals 5 left parenthesis x minus 2 right parenthesis

y−3=−15(x−2)
y minus 3 equals negative Start Fraction 1 over 5 End Fraction left parenthesis x minus 2 right parenthesis

y+3=−15(x+2)

Answer 1

To find a line that is perpendicular to the line given by the equation \( y = 5x - 2 \) and passes through the point \( (2, 3) \), we first need to determine the slope of the given line.

The slope of the line \( y = 5x - 2 \) is \( 5 \). The slope of a line that is perpendicular to this will be the negative reciprocal of \( 5 \). The negative reciprocal of \( 5 \) is \( -\frac{1}{5} \).

Now we will use the point-slope form of a line, given by the equation \( y - y_1 = m(x - x_1) \), where:
- \( (x_1, y_1) \) is the point the line passes through,
- \( m \) is the slope.

Plugging in the point \( (2, 3) \) and the slope \( -\frac{1}{5} \), we have:
\[
y - 3 = -\frac{1}{5}(x - 2)
\]

This equation matches the second response option you provided:
\[
y - 3 = -\frac{1}{5}(x - 2)
\]

Thus, the correct answer is:
**y − 3 = −\frac{1}{5}(x − 2)**.