What is the equation of a line perpendicular to y = -5x +3?(1 point) Responses y = 15 x + 7 y = 1 fifthx + 7 y = -5x + 6 y = -5x + 6 y = -15 x + 9 y = -1 fifthx + 9 y = 5x + 3

1 answer

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

Lines that are perpendicular to each other have slopes that are negative reciprocals. Therefore, the slope \( m \) of the line that is perpendicular to the given line can be calculated as follows:

\[ m = -\frac{1}{-5} = \frac{1}{5} \]

Now, using the slope of \( \frac{1}{5} \), we can express the equation of a line in point-slope form. However, since we do not have a specific point to use, we can just write the general form of the line:

\[ y = \frac{1}{5}x + b \]

where \( b \) is the y-intercept, which can be any value depending on the specific line we want.

Among the given responses, the line with a slope of \( \frac{1}{5} \) is:

\[ y = \frac{1}{5}x + 7 \]

Thus, the equation of a line that is perpendicular to \( y = -5x + 3 \) is:

Answer: \( y = \frac{1}{5}x + 7 \)