Can you identify a parallel or perpendicular equation and type the correct code? Please remember to type in ALL CAPS with no spaces.*
Puzzle #3
1: Find on equation that is
parallel to
2: Find an equation that
is perpendicular to:
answer choices
A: 2 B: C: -3
YEX-Yox. Yux.
D: 5 E: 3 F: 4
Ye, Y X-
G: H: I: -2
y=-2x Il y --4x YEX.
Yax.
4x. 3y = 12
4: Find an equahon that is
perpendicular to
3: Find an equation
that is parallel to
Type the 4-
letter code into
the answer
box. All CAPS
no spaces.
2x5y = 10
HCIA

1) C. -3/4·x + 3

2) E. 3/4·x - 1

3) I. -2/5·x + 3

4) A. 2/5·x - 1

Step-by-step explanation:

1) The points on the given line are;

(4, -2), (0, 1), and (-4, 4)

The slope of the line = (1 - (-2))/(0 - 4) = -3/4

The y-intercept = (0, 1)

The equation of the line is therefore, y = -3/4·x + 1

The line parallel to the given line has equal slope to the line, and the different y-intercept, therefore, the correct option for the line parallel to the given line is therefore;

C. -3/4·x + 3

2) The equation of the given line is 4·x + 3·y = 12

Rewriting the equation in slope and intercept form gives;

4·x + 3·y = 12

3·y = 12 - 4·x

y = 12/3 - 4/3·x = 4 - 4/3·x

The slope, m₁, of the given line = -4/3

The y-intercept = (0, 4)

A line perpendicular to the given line, has a slope, m₂ = -1/m₁

Where, m₁ = The slope of the given line

The slope of the perpendicular to the given line is therefore;

m₂ = -1/m₁ = -1/(-4/3) = 3/4

Therefore, the equation of the line perpendicular to the given line is of the form

y =  3/4·x + c, where c is a real number

The correct option for the line perpendicular to the given line is therefore; E. 3/4·x - 1

3) The equation of the given line is 2·x + 5·y = 10

Rewriting the equation in slope and intercept form gives;

2·x + 5·y = 10

5·y = 10 - 2·x

y = 10/5 - 2/5·x = 2 - 2/5·x

y = 2 - 2/5·x

The slope, m₂, of a parallel line to the given line is equal to that of the given line, m₁

Whereby from the above equation, we have, m₁ = -2/5

Therefore, m₂ = m₁ = -2/5

The general equation of a line parallel to the given line is therefore;

y = m₂·x + c = -2/5·x + c, where c is a real number

The correct option for the line parallel to the given line is therefore;

I. -2/5·x + 3

4) The points (intercepts) on the given line are (2, 0), and (0, 5)

The slope of the given line is therefore;

(5 - 0)/(0 - 2) = -5/2

The slope of the perpendicular line, m₂ = -1/m₁, gives;

m₂ = -1/(-5/2) = 2/5

The general form equation of the equation of the perpendicular line to the given line is therefore given as follows;

y = m₂·x + c = 2/5·x + c, where c is a real number

The correct option for the line perpendicular to the given line is therefore;

A. 2/5·x - 1.