Question

"Write an equation of the line that is perpendicular to the line represented by the equation ‘y = (1/2)x + 5’ and contains point P(3, -4). Write the equation for the line in point-slope form."

Answer 1

To find the equation of a line that is perpendicular to the line represented by the equation 'y = (1/2)x + 5' and contains point P(3, -4), use the point-slope form of a linear equation with a slope of -2 and the coordinates of the point.

Step-by-step explanation:

To find the equation of a line that is perpendicular to the line represented by the equation 'y = (1/2)x + 5' and contains point P(3, -4), we need to determine the slope of the perpendicular line.

The given line has a slope of 1/2, so the slope of the perpendicular line will be the negative reciprocal of 1/2, which is -2.

Using the point-slope form of a linear equation, we plug in the values of the point P(3, -4) and the slope -2 to get the equation: y - y1 = m(x - x1), where x1 = 3, y1 = -4, and m = -2.

Substituting the values, we get: y - (-4) = -2(x - 3).

Simplifying this equation gives us the equation of the line in point-slope form as y + 4 = -2(x - 3).