Write an equation of the line that passes through (1,2) and is perpendicular to the line y= 1/3x+4

The equation of the line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4) is (y = -3x + 5) and this can be determined by using the given data.

Given :

The line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4).

The following steps can be used in order to determine the equation of the line:

Step 1 - When two lines are perpendicular to each other then their slopes are:

mm' = 1

where m and m' are the slopes of the lines.

Step 2 - So, the slope of the line which is perpendicular to the line (y = 1/3x + 4) is:

m' = -3

Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:

Step 4 - Simplify the above equation.

y = -3x + 5

For more information, refer to the link given below:

link

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or

Perpendicular line's slope =   (flip the sign from + to -, and flip the fraction)

Slope =

Perpendicular line's slope =  (flip the sign from - to +, and flip the fraction)

y = 1/3x + 4        The slope is 1/3, so the perpendicular line's slope is or -3.

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

y = -3x + b       To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself

2= -3(1) + b     Add 3 on both sides to get "b" by itself

2 + 3 = -3 + 3 + b

5 = b

y = -3x + 5