Equation of a Straight Line: Using the angle formed by the line with the axes

Examples with solutions for Equation of a Straight Line: Using the angle formed by the line with the axes

Exercise #1

Two lines have slopes of 6 -6 and 12 \frac{1}{2} .

Which of the lines forms a smaller angle with the x-axis?

Video Solution

Step-by-Step Solution

We will use the formula:

m=tanα m=\tan\alpha

Let's check the slope of minus 6:

6=tanα -6=\tan\alpha

tan1(6)=α \tan^{-1}(-6)=\alpha

80.53=α -80.53=\alpha

18080.53= 180-80.53=

99.47=α1 99.47=\alpha_1

Let's check the slope of one-half:

12=tanα \frac{1}{2}=\tan\alpha

tan1(12)=α \tan^{-1}(\frac{1}{2})=\alpha

26.56=α2 26.56=\alpha_2

\alpha_1 > \alpha_2

Answer

The line with a slope of 12 \frac{1}{2}

Exercise #2

Two lines haves slopes of -3 and -6.

Which of the lines forms a greater angle with the x axis?

Video Solution

Answer

The line whose slope is -3 forms the greater angle.

Exercise #3

Two straight lines have slopes of2,12 2,\frac{1}{2} .

Which of the lines forms a larger angle with the x axis?

Video Solution

Answer

The straight line with a slope of 2 forms the largest angle.

Exercise #4

Which algebraic equation represents a straight line that passes through the point (3,14) (3,14) and creates an angle of 135 degrees with the positive part of the x axis?

Video Solution

Answer

y+x=17 y+x=17

Exercise #5

Choose the equation that represents a straight line that passes through the point (2,2) (2,2) and creates an angle of 180 degrees with the positive part of the x axis.

Video Solution

Answer

y=2 y=2

Exercise #6

Find the slope of a line that makes an angle of 100 degrees with the positive part of the xaxis, and indicate whether the line is ascending or descending.

Video Solution

Answer

m=5.67 m=-5.67 decreasing

Exercise #7

Which function represents a straight line that passes through the point (3,5) (-3,-5) and creates an angle of 45 degrees with the positive part of the x axis?

Video Solution

Answer

y=x2 y=x-2

Exercise #8

Choose the algebraic equation that describes a straight line that passes through the point (9,2) (-9,2) and forms a 30-degrees angle with the positive part of the x axis.

Video Solution

Answer

3y3x=6+93 3y-\sqrt{3x}=6+9\sqrt{3}