Question

15. Find to the nearest degree the measure of the acute angle that the graph

of y = 2x - 4 makes with the x-axis.​

Answer 1

Check the picture below.

make sure your calculator is in Degree mode.

Answer 2

63°.

Explanation:

To find the angle we can use as limits of the figure the intersection of y = 2x-4 with the x-axis and any point at the right of it.

To find the intersection of y = 2x-4 with the x-axis we do y=0:

0 = 2x-4

4 = 2x

x = 4/2 = 2.

Then, the left limit is (2,0). Now, let's use x=3 as an example to find the right limit:

y = 2(3)-4

y = 6-4

y = 2.

Then, the right limit is (3,2). You can see it in graph below. As you can see, the acute angle
`\alpha` we are searching for can be calculated with the horizontal and vertical distances of the triangle limited by the two points, the line and the x-axis. So,

`tan(\alpha) = (2)/(1)`

`tan(\alpha) = 2`

`\alpha = tan^(-1)(2)`

`\alpha = 63.43\textdegree \approx 63\textdegree`.