Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

y – 3 = negative one-fifth(x + 2); (–2, 7)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of a line that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.

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

Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line:
y - y1 = m(x - x1)

Using the point (-2, 7) and the slope 5, we have:
y - 7 = 5(x - (-2))

Simplifying this equation gives us the equation of the line:
y - 7 = 5(x + 2)

So, the equation of the line that is perpendicular to the given line and passes through the point (-2, 7) is y - 7 = 5(x + 2).