Question

The equation of line CD is y = 3x - 3. Write an equation of a line perpendicular to line CD in slope-intercept form that contains point (3, 1). (5 points)

y = 3x + 0
y = 3x - 8
Tl
Tom

Answer 1

y= -1/3x + 2

Explanation:

i took the test

Answer 2

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 negative reciprocals of each other. (flip the sign +/- and the fraction/switch the numerator and the denominator)

For example:

Slope = -2 or
`-(2)/(1)`

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

Slope =
`(1)/(3)`

Perpendicular line's slope =
`-(3)/(1)` or -3 (flip the sign from + to -, flip fraction)

y = 3x - 3 The slope is 3, so the perpendicular line's slope is
`-(1)/(3)`.

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

y = mx + b

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

`1=-(1)/(3) (3)+b`

1 = -1 + b Add 1 on both sides to get "b" by itself

1 + 1 = -1 + 1 + b

2 = b

`y=-(1)/(3) x+2`