Find the equation of a line passing through the point (-1,2) and making an angle 13 degrees with the x-axis.
To be given this kind of question means that you must have learned that the slope of a line is equal to the tangent of the angle that the line makes with the x-axis.
so tan 13º = .2309
then y-2 = .2309(x+1)
take it from there
To find the equation of a line passing through a given point and making an angle with the x-axis, you need to find the slope of the line first.
The slope of a line making an angle θ with the x-axis can be determined by taking the tangent of that angle.
Given that the angle is 13 degrees, we can calculate the slope as follows:
slope = tan(13°)
Using a calculator, we find that tan(13°) ≈ 0.224
Now, we have the slope (m) of the line, which is 0.224, and the point (-1, 2) it passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values:
y - 2 = 0.224(x - (-1))
y - 2 = 0.224(x + 1)
Expanding and simplifying:
y - 2 = 0.224x + 0.224
y = 0.224x + 0.224 + 2
y = 0.224x + 2.224
Therefore, the equation of the line passing through the point (-1, 2) and making an angle of 13 degrees with the x-axis is y = 0.224x + 2.224.
To find the equation of a line passing through a given point and making an angle with the x-axis, we need to use the slope-intercept form of a line, y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the line makes an angle of 13 degrees with the x-axis, we can determine the slope using trigonometry. The slope is defined as the tangent of the angle.
Let's find the slope:
slope (m) = tan(angle)
m = tan(13°)
Using a calculator, we get m ≈ 0.2287.
Now, we have the slope (m) and the given point (-1,2). We can substitute these values into the slope-intercept form (y = mx + b) to find the y-intercept (b).
2 = (0.2287)(-1) + b
2 = -0.2287 + b
b = 2 - (-0.2287)
b = 2.2287
Now we have the slope (m = 0.2287) and the y-intercept (b = 2.2287). Plugging these values into the slope-intercept form (y = mx + b), we get the equation of the line:
y = 0.2287x + 2.2287
Therefore, the equation of the line passing through the point (-1, 2) and making an angle of 13 degrees with the x-axis is y = 0.2287x + 2.2287.