Question

What is the equation of the line through point (2,1) and perpendicular to line through (-4,1) and (3,-2)?

Answer 1

The equation of the line that is perpendicular to the line passing through (-4,1) and (3,-2) and passes through the point (2,1) is y = (7/3)x - 11/3.

Step-by-step explanation:

To find the equation of the line that is perpendicular to the line passing through (-4,1) and (3,-2) and passes through the point (2,1), we need to follow these steps:

1. Find the slope of the given line by using the formula: slope = (y2 - y1) / (x2 - x1). In this case, (-4,1) and (3,-2) are our two points. Substitute the values into the formula:
2. slope = (-2 - 1) / (3 - (-4)) = -3/7
3. The slope of the perpendicular line will be the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is 7/3.
4. Now that we have the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1,y1) is the given point.
5. Substitute the values into the equation:
6. y - 1 = (7/3)(x - 2)
7. Simplify and rewrite the equation in slope-intercept form (y = mx + b), where b is the y-intercept:
8. y = (7/3)x - 11/3

Therefore, the equation of the line that is perpendicular to the line passing through (-4,1) and (3,-2) and passes through the point (2,1) is y = (7/3)x - 11/3.