Equation of a Line Worksheet

**Page 1**

1.

Which of the following equations does not represent a straight line?

a. | $y$ = - $\frac{1}{10}$$x$ + 9 | ||

b. | $\mathrm{xy}$ = 9 | ||

c. | 10$x$ - $y$ - 8 = 0 | ||

d. | ($y$ - 9) = 10($x$ - 8) |

[Equation of a straight line in slope-intercept form.]

(

[Equation of a straight line in point-slope form.]

10

[Equation of a straight line in standard form.]

Correct answer : (2)

2.

Which of the following represents the point-slope form of an equation of a line?

a. | $y$ = $\mathrm{mx}$ + $b$ | ||

b. | $\frac{x}{a}$ + $\frac{y}{b}$ = 1 | ||

c. | $y$ - $y$ _{1} = $m$($x$ - $x$_{1}) | ||

d. | A$x$ + B$y$ = C |

Correct answer : (3)

3.

Which of the following lines is perpendicular to the line $y$ = 8$x$ + 7?

a. | $y$ = - $x$ + 7 | ||

b. | $y$ = - $\frac{1}{8}$$x$ | ||

c. | $y$ = - 7$x$ + 8 | ||

d. | $y$ = $\frac{1}{7}$$x$ |

The slope of the line

[Find the slope of the line using

If

Equation | Slope |

- - 7 - 1 |

So, the line

Correct answer : (2)

4.

Determine whether the statement is true or false. The line whose equation is $x$ - 5$y$ + 27 = 0 passes through (- 2, 5) and has a slope $\frac{1}{5}$ .

a. | False | ||

b. | True |

[Equation of the line.]

[Slope-intercept form of the line.]

Slope =

[Slope of

Substitute (- 2, 5) in

- 2 - 5 (5) + 27 = 0

0 = 0, which is always true.

So, the given statement is true.

Correct answer : (2)

5.

Which of the following two lines are perpendicular?

I. $y$ = 6$x$

II. $y$ = - 6$x$

III. $y$ = $\frac{1}{6}$$x$

IV. $y$ = - $x$

IV. $y$ = - $x$

a. | I and II | ||

b. | II and IV | ||

c. | II and III | ||

d. | III and I |

Equation | Slope | |

6 - 6 - 1 |

Two lines are perpendicular if the product of their slopes is - 1.

The product of the slopes of the lines

So, the lines II and III are perpendicular.

Correct answer : (3)

6.

Which of the following statements is true for the graph of the function $y$ = 3?

a. | The graph of $y$ = 3 in the coordinate plane is a single point (0, 3). | ||

b. | The graph of $y$ = 3 is a line parallel to the $y$-axis, at a distance of 3 units to the right of it. | ||

c. | The graph of $y$ = 3 is a line parallel to the $x$-axis, at a distance of 3 units above the $x$-axis. | ||

d. | The graph of $y$ = 3 is a line parallel to the $x$-axis, at a distance of 3 units below the $x$-axis. |

The graph of

So, the graph of

Correct answer : (3)

7.

Find the equation of the line perpendicular to 5$x$ - 4$y$ = 9 and having the same $y$ - intercept.

a. | 5$x$ - 4$y$ + 9 = 0 | ||

b. | 16$x$ - 20$y$ + 45 = 0 | ||

c. | 16$x$ + 20$y$ + 45 = 0 | ||

d. | 36$x$ + 45$y$ + 20 = 0 |

[Equation of a line.]

[Rewrite it in

So, the slope,

Slope of the perpendicular line = -

The equation of the perpendicular line is:

[

20

[Multiply both sides by 20.]

16

[Simplify.]

Correct answer : (3)

8.

Find the equation of the line passing through (1, 0) and parallel to the line passing through (0, 0) and (10, - 5) .

a. | 4$x$ + 2$y$ - 1 = 0 | ||

b. | $x$ + 2$y$ - 4 = 0 | ||

c. | $x$ - 2$y$ + 1 = 0 | ||

d. | $x$ + 2$y$ - 1 = 0 |

Slope =

Slope of the line parallel to the given line = -

[Parallel lines slopes are equal.]

So, equation of the parallel line is,

[Slope-intercept form.]

This line passes through the point (1, 0).

0 = -

[Simplify.]

Therefore, the equation of the line is

2

[Multiply both sides by 2.]

Correct answer : (4)

9.

Which of the following lines are parallel?

I. $y$ = $\frac{1}{2}$$x$

II. $y$ = $\frac{1}{5}$$x$ + 2

III. $y$ = $\frac{1}{2}$$x$ + $\frac{1}{5}$

IV. $y$ = - 5$x$ + $\frac{1}{2}$

a. | II and II | ||

b. | I, II and III | ||

c. | II, III and IV | ||

d. | I and III |

Therefore, the two lines are parallel.

Equation | Slope |

- 5 |

Slopes of the lines

So, the lines I and III are parallel.

Correct answer : (4)

10.

What is the equation of the line passing through the point (4, 5) and perpendicular to the line $y$ = 3$x$ + 8?

a. | $x$ + 4 = - 3($y$ - 5) | ||

b. | $y$ - 5 = - $\frac{1}{3}$($x$ - 4) | ||

c. | $x$ - 4 = 3($y$ - 5) | ||

d. | $y$ + 5 = - $\frac{1}{3}$($x$ - 4) |

Slope of the line

[Compare with the equation in step 1.]

Slope of the line perpendicular to

[Product of the slopes of perpendicular lines is -1.]

The equation of the line passing through the point (

Point (

[Substitute

The equation of the line passing through the point (4, 5) is

Correct answer : (2)

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