Question

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

Answer 1

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 $\frac{2}{1}$

Perpendicular line's slope = $-\frac{1}{2}$   (flip the sign from + to -, and flip the fraction)

Slope = $-\frac{3}{4}$

Perpendicular line's slope = $\frac{4}{3}$  (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 $-\frac{3}{1}$ 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