A line has a y-intercept of 5 and makes and angle of inclination of 55 degrees with the x-axis what is the slope?

Answer 1

Plot the point (0, 5) in the y-axis and label it A. From the point A, draw a line in such way that the inclination angle of 55 degrees to be formed, and label the point of intersection of this line with x-axis with B(x, 0). Label the origin (0, 0) with O. A right triangle is formed, the triangle AOB, where the angle O is 90 degrees (because you know that x-axis and y-axis are two perpendicular lines), the inclination angle ABO is 55 degrees, and the distance AO is |5 - 0| = |5| = 5. Since the sum of angle OAB and the angle ABO is 90 degrees, the measure of the angle OAB = 90 - 55 = 35 degrees. Now that you know two angles, and one of the opposite side to one of these angles, by using the Law of Sines you can find the other opposite side to the other angle. The distance of this opposite side will be, |x - 0| = |x| = x. So you have:

5/sin 55 degrees = x/sin 35 degrees Cross multiply;

5(sin 35 degrees) = x(sin 55 degrees) Divide by sin 55 degrees to both sides;

[5(sin 35 degrees]/sin 55 degrees = x Use calculator to find x, put your calculator in degree mode, and type:(5(sin(35))/sin(55), and press Enter. You'll find 3.5010. So,

x = 3.5, which is the x-cordinate of the point B(3.5, 0)

Now that you have the coordinates of two points on the line, the point A(0,5) and the point B(3.5, 0), you are able to find the slope m of this line.

m = (y2 - y1)/(x2- x1) = (5 - 0)/(0 - 3.5) = 5/-3.5 = - 5/3.5 or you can turn 3.5 into a fraction by pressing Math Enter Enter in the calculator (Texas Instrument)

- 5/(7/2) = - (5)(2/7) = - 10/7

The anser is: the slope is -10/7.