The given slope is `m = -1` .
Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:
`tan theta = m`
where `theta` is the angle measured counterclockwise from the positive x-axis going to the right of the line. And its range of values is from 0 to 180 degree only `(0^o lt= theta lt=180^o)` .
Plugging in the value of m, the...
The given slope is `m = -1` .
Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:
`tan theta = m`
where `theta` is the angle measured counterclockwise from the positive x-axis going to the right of the line. And its range of values is from 0 to 180 degree only `(0^o lt= theta lt=180^o)` .
Plugging in the value of m, the formula becomes:
`tan theta = -1`
Then, take the inverse of tangent to isolate theta.
`theta =tan ^(-1)`
`theta = -pi/4 rad =-45^o`
Take note that when the computed value is negative, to get value of angle of inclination in the interval `0^o lt= thetalt=180^o` , add 180 degree (pi rad).
`theta = -pi/4 + pi = (3pi)/4` rad
`theta = -45^o + 180^o = 135^o`
Therefore, in radians, the angle of inclination is `(3pi)/4` rad. And in degree, the angle of inclination is `135^o` .
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