What is the equation of the line perpendicular to the line y = 49x + 2 that passes through the point (4, 3)?

To find the equation of the line that is perpendicular to the line y = 49x + 2 and passes through the point (4, 3), we first need to determine the slope of the given line.

The equation of the line is in the slope-intercept form y = mx + b, where m represents the slope. From the equation y = 49x + 2, we see that the slope m is 49.

For two lines to be perpendicular, the product of their slopes must equal -1. Therefore, if the slope of the given line is 49, the slope of the line perpendicular to it will be:

• m_{perpendicular} = -1/m_original = -1/49

Now that we have the slope of the perpendicular line, we can use the point-slope form of a line’s equation, which is given by y – y₁ = m(x – x₁), where (x₁, y₁) is a point on the line, and m is the slope.

Plugging in the slope -1/49 and the point (4, 3), we get:

y - 3 = -1/49(x - 4)

To convert this into slope-intercept form, we can simplify:

y - 3 = -1/49x + 4/49

y = -1/49x + 4/49 + 3

y = -1/49x + 4/49 + 147/49

y = -1/49x + 151/49

So, the equation of the line perpendicular to y = 49x + 2 that passes through the point (4, 3) is:

y = -1/49x + 151/49