Slope of the Line Equation Worksheet

**Page 1**

1.

If A = (4, 3), B = (5, 4) and C = (8, 7), then which of the following is correct?

a. | Triangle ABC is equilateral triangle | ||

b. | Triangle ABC is right triangle | ||

c. | Triangle ABC is scalane triangle | ||

d. | A, B, and C are collinear |

[Definition.]

The points are A(4, 3), B(5, 4), C(8, 7)

Slope of line joining A, B =

Slope of line joining B, C =

Here slope of line joining A, B = slope of line joining B, C = 1

Hence, the points A, B, C are collinear.

Correct answer : (4)

2.

What is the slope of a line on which for every point the $x$ coordinate is same?

a. | Infinitely small | ||

b. | Infinitely large | ||

c. | Undefined |

So, let A(

Slope of line L = Slope of line joining A,B =

[Use the slope formula.]

=

=

[Division by 0 is not defined]

Correct answer : (4)

3.

Find the slope of the line passing through the points A (7, 9) and B (12, 12).

a. | $\frac{3}{5}$ | ||

b. | $\frac{19}{21}$ | ||

c. | 8 | ||

d. | - $\frac{19}{21}$ |

=

[Use the slope formula.]

Correct answer : (1)

4.

If $a$ ≠ $b$, then what is the slope of the line joining the points P(5$a$, 6$b$) and Q(6$b$, 5$a$)?

a. | Independent of $a$, $b$ | ||

b. | Dependent of $a$ | ||

c. | Dependent of $a$, $b$ | ||

d. | Dependent of $b$ |

[Use the slope formula.]

= - (

Slope of the line is "- 1" which is independent of both

Correct answer : (1)

5.

What is the slope of the line on which for every point the ordinate is same?

a. | Undefined | ||

b. | Infinitely large | ||

c. | Infinitely small |

So, let P(

Slope of line L = Slope of line joining P,Q =

=

[Use the slope formula.]

=

Correct answer : (2)

6.

Find the angle of inclination of a line whose slope is - $\sqrt{3}$.

a. | $\frac{5\pi}{4}$ | ||

b. | $\frac{\pi}{4}$ | ||

c. | $\frac{\pi}{3}$ | ||

d. | $\frac{2\pi}{3}$ |

tan θ = -

[Use the definition of slope.]

tan θ = -

[0 ≤ θ < π]

θ =

Correct answer : (4)

7.

If $a$ ≠ - 1, then what is the slope of the line joining the points (- 4$a$, 4) , ($a$^{2} + 4, $a$^{2})?

a. | $\frac{2-a}{a+2}$ | ||

b. | $\frac{a+2}{2-a}$ | ||

c. | $\frac{a-2}{a+2}$ | ||

d. | $\frac{a+2}{a-2}$ |

Slope of line joining P, Q =

[Use the slope formula.]

=

=

[Cancel the common factor.]

Slope of line joining P, Q is

Correct answer : (3)

8.

If $t$ > 1and $m$ is the slope of the line joining the points ($\frac{2}{{t}^{2}}$ , $\frac{4}{t}$) and (2$t$^{2} , 4$t$), then which of the following is correct?

a. | $m$ =1 | ||

b. | $m$ < 1 | ||

c. | $m$ =2 | ||

d. | $m$ > 1 |

Slope of line joining P,Q =

[Use the slope formula.]

=

So,

[Cancel the common factor.]

[ For

So,

Correct answer : (2)

9.

Find the values of $k$ such that the points ($k$ + 2, 2), (2$k$ + 2, 4) and (2$k$ + 3, 2$k$ + 1) are collinear.

a. | - $\frac{1}{2}$ , 2 | ||

b. | - $\frac{1}{2}$ , -2 | ||

c. | $\frac{1}{2}$ , -2 | ||

d. | $\frac{1}{2}$ , 2 |

Slope of line joining A, B = slope of line joining B,C .

[The three points A, B, C are collinear.]

[Use the slope formula.]

2

(2

[Factor.]

Correct answer : (1)

10.

What is the slope of the line 3$x$ + 4$y$ + 14 = 0?

a. | - $\frac{4}{3}$ | ||

b. | $\frac{14}{3}$ | ||

c. | $\frac{7}{2}$ | ||

d. | - $\frac{3}{4}$ |

[Solve for

Slope of the line =

[The above equation is in the slope intercept form

Correct answer : (4)