Question

5.

A straight line M is perpendicular to y = 3x + 5 and passes through the point (3,7),
Find the equation of the line M.

Answer 1

y=-1/3x+8

Explanation:

Given that the line is perpendicular to y = 3x + 5 and passes through the point (3,7), we can find the slope of the line by finding the negative reciprocal of the slope of y = 3x + 5.

The slope of y = 3x + 5 is 3, so the slope of the perpendicular line will be the negative reciprocal of 3, which is -1/3.

Next, we can use the point-slope form of a line to find the equation of the line. The point-slope form of a line is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We can plug in the values we have:

y - 7 = -1/3(x - 3)

Expanding the right side:

y - 7 = -1/3x + 1

Adding 7 to both sides:

y = -1/3x + 8

So the equation of the line is:

y = -1/3x + 8

Answer 2

This is what I think (I'm not sure, so this is the best of my ability what I can find).

The equation of the line M is y = -3x + 7. This can be found by considering the point-slope form of an equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. In this case, the given point is (3,7) and the slope of the line is -3 since it is perpendicular to y = 3x + 5 (the slope of a perpendicular line is the negative reciprocal of the original). Therefore, the equation of the line M is y - 7 = -3(x - 3), which simplifies to y = -3x + 7.