PARALLEL PERPENDICULAR AND INTERSECTING LINES

Problem 1 :

Line A passes through the points (4, 6) and (-3, 2). What is the slope of a line that is parallel to line A?

Solution:

Line A passes through the points (4, 6) and (-3, 2).

Problem 2 :

Line B passes through the points (-1, 0) and (4, -7). What is the slope of a line that is parallel to line B?

Solution:

Line B passes through the points (-1, 0) and (4, -7).

Problem 3 :

Line C passes through the points (5, -10) and (15, 20). What is the slope of a line that is perpendicular to line C?

Solution:

Line C passes through the points (5, -10) and (15, 20).                                                

Problem 4 :

Line D passes through the points (12, 3) and (15, 6). What is the slope of a line that is perpendicular to line D?

Solution:

Line D passes through the points (12, 3) and (15, 6).     

Problem 5 :

Find an equation of a line that is parallel to y = 2x + 4 with a y-intercept at (0, -7).

Solution:

When  two line are parallel, their slopes are equal.

y = 2x + 4 

Slope m = 2

y = mx + b

Substitute (x, y) = (0, -7)

-7 = 2(0) + b

b = -7

So, the equation of the line as y = 2x - 7.

Problem 6 :

Solution:

So, the equation of the line as

Problem 7 :

Find an equation of a line that is parallel to y = 3x - 14 that passes through the point (4, 5). 

Solution:

y = 3x - 14

Slope m = 3

y - y₁ = m(x - x₁)

Substitute (x₁, y₁) = (4, 5).

y - 5 = 3(x - 4)

y - 5 = 3x - 12

y = 3x - 12 + 5

y = 3x - 7

Problem 8 :

Solution:

So, the equation of the line as

Problem 9 :

Find an equation for the line that is perpendicular to y + 2 = 2(x - 5) with a y-intercept at (0, -7).

Solution:

y + 2 = 2x - 10

y = 2x - 12

Slope m = 2

So, the equation of the line as

Problem 10 :

Solution:

So, the equation of the line as