Find the gradient of the straight lines and their angles of inclination A(-2, 0) and B(6,-4)?

All_for_one

2 years ago

We can find the gradient of a line using the formula:

dx
dy

=
x
2

−x
1


y
2

−y
1





where:

dx
dy

is the gradient of the line
(x
1

,y
1

) and (x
2

,y
2

) are the coordinates of two points on the line
Given the points A(−2,0) and B(6,−4), we can find the gradient as follows:

dx
dy

=
6−(−2)
−4−0

=−
8
4

=−
2
1



Therefore, the gradient of the line passing through A(−2,0) and B(6,−4) is −
2
1

.

The angle of inclination of a line is the angle between the line and the positive x-axis. You can find the angle of inclination using the arctangent function:

θ=arctan(
dx
dy

)

where:

θ is the angle of inclination in radians
dx
dy

is the gradient of the line
Given the gradient
dx
dy

=−
2
1

, we can find the angle of inclination as follows:

θ=arctan(−
2
1

)≈−30
∘


Therefore, the angle of inclination of the line passing through A(−2,0) and B(6,−4) is approximately −30
∘
.

In conclusion, the gradient of the line passing through A(−2,0) and B(6,−4) is −
2
1

, and the angle of inclination of the line is approximately −30∘
.