Write the equation of a line that is perpendicular to the given line and that passes through the given point. y – 3 = (x + 2); (–2, 3) A. y + 3 = – 3/8(x – 2) B. y – 3 = – 3/8(x + 2) C. y – 2 = –(x + 3) D. y + 3 = 3/8 (x – 2)

Question

A. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is 5.
B. The functions have the same y-intercept. The second function is steeper than y = |x|.
C. The two functions are the same.
D. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –5. The functions have the same shape. The y -intercept of y = | x | is 0, and the y -intercept of the second function is –5.

Answer 1

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

The given line has a slope of 1, since it is in the form y - mx + c and the coefficient of x is 1.

The negative reciprocal of 1 is -1.

So, the slope of the perpendicular line is -1.

We also know that the line passes through the point (-2, 3).

Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we can substitute the values into the equation.

y - 3 = -1(x + 2)

Simplifying the equation gives us:

y - 3 = -x - 2

Rearranging the equation to the standard form gives us:

y + x = 1

So, the equation of the line that is perpendicular to the given line and passes through the point (-2, 3) is y + x = 1.