find the gradient of the joining 3,7 and 6,9. find the acute angle it make the positive x-axis.
well, I assumed you were looking for an answer, and not just stopping by to chat.
The gradient is the slope of the line: (9-7)/(6-3) = 2/3
The angle θ is such that tanθ = 2/3
To find the gradient of a line joining two points, you can use the formula:
Gradient (m) = (Change in y)/(Change in x)
Let's denote the first point as (x1, y1) = (3, 7) and the second point as (x2, y2) = (6, 9).
Change in y = y2 - y1 = 9 - 7 = 2
Change in x = x2 - x1 = 6 - 3 = 3
Gradient = (Change in y)/(Change in x) = 2/3
Now, let's find the acute angle this line makes with the positive x-axis. To do this, you can use the inverse tangent function (arctan) of the gradient.
Angle = arctan(Gradient)
Using a calculator or math software, you can find:
Angle = arctan(2/3) ≈ 33.69 degrees
Therefore, the acute angle that the line makes with the positive x-axis is approximately 33.69 degrees.