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.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer