Question

A line is perpendicular to y = -5x + 3 and contains the point (2,7). Find an equation for this line.

A. y = 5x + 3
B. y = -5x + 7
C. y = 5x - 7
D. y = -5x - 7

Answer 1

To find the equation for a line that is perpendicular to y = -5x + 3 and contains the point (2,7), we need to find the negative reciprocal of the given line's slope and substitute it into the point-slope form of the equation.

Step-by-step explanation:

To find the equation for a line that is perpendicular to y = -5x + 3 and contains the point (2,7), we need to find the slope of the given line and then find the negative reciprocal of that slope.

1. The given equation is in the form y = mx + b, where m is the slope. In this case, the slope is -5.
2. The negative reciprocal of -5 is 1/5.
3. Using the point-slope form, we can substitute the slope and the coordinates of the given point into the equation: y - y1 = m(x - x1). Therefore, the equation for the line is y - 7 = (1/5)(x - 2).
4. Simplifying, we get the equation y = (1/5)x + 7/5, which can also be written as y = 1/5x + 1.4.