Final answer:
The equation of the line through (2, -2) which is perpendicular to the line y = x/4 + 7 is y = -4x + 6. This is found using the perpendicular slope -4 and the given point in the point-slope formula.
Step-by-step explanation:
The subject of this question is finding the equation of a line that is perpendicular to a given line and passes through a specified point. In this case, we are given the line y = x/4 + 7 and the point (2, -2). To find a line perpendicular to the given line, we first need to determine the slope of the given line which is 1/4. The slope of a perpendicular line will be the negative reciprocal of this, which is -4. Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope of the perpendicular line and the given point to find the y-intercept.
Here's a step-by-step breakdown:
- Original line's slope: 1/4
- Perpendicular line's slope (m): -4
- Use the point-slope form with the given point (2, -2): y - (-2) = (-4)(x - 2)
- Simplify the equation: y + 2 = -4x + 8
- Isolate y to put it in slope-intercept form: y = -4x + 6
Therefore, the equation of the line perpendicular to y = x/4 + 7 passing through (2, -2) is y = -4x + 6.