Write the equation of a line that is perpendicular to the given line and that passes through the given point. y – 3 = 1/5 (x + 2); (–2, 7) (1 point)

Answer 1

The equation of the given line is y - 3 = (1/5)(x + 2).
To find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope of the given line.

The slope of the given line is 1/5, so the negative reciprocal is -5/1, which is -5.

Now we have the slope (-5) and the point (-2, 7). We can use the point-slope form of the equation of a line to find the equation of the line perpendicular to the given line.

The equation of the line can be written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Using the point (-2, 7) and the slope -5, the equation of the line perpendicular to the given line is:

y - 7 = -5(x - (-2))

Simplifying this equation, we get:

y - 7 = -5(x + 2)

Answer 2

y = 5x + 7 y = 5 x + 7 y = 5x + 17 y = 5 x + 17 y = x – 2 y = Image with alt text: one-fifth x – 2 y = –2x + 3

Answer 3

Sorry, I made a mistake in my previous response. Let's correct it:

The given line has a slope of 1/5.

To find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope of the given line, which is -5/1, also known as -5.

Now, we can use the point-slope form of the equation of a line to find the equation of the line perpendicular to the given line.

Using the point (-2, 7) and the slope -5, the equation of the line perpendicular to the given line is:

y - 7 = -5(x - (-2))

Simplifying this equation, we get:

y - 7 = -5(x + 2)
y - 7 = -5x - 10
y = -5x - 3