what is the angle of inclination for 7x + 3y = 9?
what is the angle of inclination for 7x + 3y = 9?
To find the angle of inclination for the equation 7x + 3y = 9, we need to rearrange the equation into the slope-intercept form, which is y = mx + b. Once we have the equation in this form, the coefficient of x, which we'll call 'm', will represent the slope of the line. The angle of inclination can be found by calculating the arctangent of the slope.
Let's start by rearranging the given equation:
7x + 3y = 9
Subtract 7x from both sides:
3y = -7x + 9
Divide both sides by 3 to solve for y:
y = (-7/3)x + 3
Now, we have the equation in slope-intercept form (y = mx + b), where the slope 'm' is -7/3.
To find the angle of inclination, we can calculate the arctangent of the slope:
angle = arctan(-7/3)
Using a scientific calculator or an online calculator, evaluate the arctangent of -7/3 to find the angle of inclination.