162,570 views
31 votes
31 votes
4 The equation of a line is y= 5x+7. (a) What is the slope of a line parallel to it? (b) What is the slope of a line perpendicular to it? (Simplify your answer.)

User Fraxel
by
2.2k points

1 Answer

19 votes
19 votes

The general form of equation of line is :

y = m(x -a ) + b

where m = slope, (a,b) = passing points

The given equation of line : y = 5x + 7

On comparing it with the general form of line

we get : a = 0, b = 7, m =5

Slope = 5

a) If the two lines are parallel then the slopes of both the lines are equal.

Let the slope of the parallel line is x

slope of the given line is 5

since, the slopes are equal thus x = 5

slope of line parallel to the line y= 5x+7. is 5

b) If the two lines are perpendicular then the product of thier slope is (-1)

Let the slope of the perpendicular line is n

since the slope of the given line is 5

so, from the above statement of slopes of perpendicular lines: 5n = -1

5n = -1

n = -1/5

n = -1/5

slope of line perpendicular to the line y= 5x+7. is -1/5

Answer:

a) slope = 5

b) slope = -1/5

User Alex Po
by
2.6k points