Respuesta :
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 [tex]\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]-\frac{1}{2}[/tex] (flip the sign from + to -, and flip the fraction)
Slope = [tex]-\frac{3}{4}[/tex]
Perpendicular line's slope = [tex]\frac{4}{3}[/tex] (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 [tex]-\frac{3}{1}[/tex] 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
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:
[tex]\rm \dfrac{1}{3}\times m' = -1[/tex]
m' = -3
Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:
[tex]\rm (y -2) = -3(x-1)[/tex]
Step 4 - Simplify the above equation.
y = -3x + 5
For more information, refer to the link given below:
https://brainly.com/question/2564656
