Question

Consider the line y = 7x-3.

What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?

Answer 1

Hello! :)

Parallel lines have the same slope.

If one line has a slope of 7, then the line parallel to it has a slope of 7 as well.

Now, perpendicular lines have slopes that are opposite reciprocals. It means we take the slope of one line, make it negative, and flop it over:

`7\\-7\\-(1)/(7)`

Hope it helps. Feel free to ask me if you have any questions.

~A determined teen

`MagicalNature`

Answer 2

Gradient of parallel line= 7

Gradient of perpendicular line
`= - (1)/(7)`

Explanation:

The equation of the line is already in slope-intercept form (y= mx +c). This means that the coefficient of x is the gradient and the constant -3 is the y-intercept of the line.

y= 7x -3

Gradient= 7

Parallel lines have the same gradient.

Thus, the slope of the line parallel to this line is also 7.

The product of the gradients of 2 perpendicular lines is -1.

(Gradient of perpendicular line)(7)= -1

Gradient of perpendicular line

= -1 ÷7

`= - (1)/(7)`