Question

Find the slope of a line a. parallel and b. perpendicular to the line y = - 3x + 8.a. Parallel:b. Perpendicular:

Answer 1

Answer:

The slope of a line parallel to the given line is -3

The slope of the line perpendicular to the given line is 1/3

Step-by-step explanation:

Given:

y = -3x + 8

To find:

a) slope of a line parallel to the given line

b) slope of a line perpendicular to the given line

a) For two lines to be parallel, their slopes will be the same

From the given equation, we will get the value of the slope

`\begin{gathered} linear\text{ equation: y = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \\ \\ comparing\text{ y = mx + b with y = -3x + 8}: \\ mx\text{ = -3x} \\ m\text{ = -3} \end{gathered}`

The slope of a line parallel to the given line is -3

b) For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the other line

The slope from the line given is -3

reciprocal of the slope = 1/-3 = -1/3

negative reciprocal = -(-1/3) = 1/3

The slope of the line perpendicular to the given line is 1/3