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Artemon [7]
2 years ago
9

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, o

r neither.
3x=4y-5 and 2/3 y=x/2+8

Mathematics
1 answer:
ss7ja [257]2 years ago
4 0

Answer:

The lines are parallel

The graph in the attached figure

Step-by-step explanation:

we have

3x=4y-5 ---> equation A

\frac{2}{3}y=\frac{x}{2}+8 -----> equation B

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Find the slope of the line A

3x=4y-5

Isolate the variable y

Adds 5 both sides

4y=3x+5

Divide by 4 both sides

y=\frac{3}{4}x+\frac{5}{4}

The slope is

m_A=\frac{3}{4}

step 2

Find the slope of line B

\frac{2}{3}y=\frac{x}{2}+8

Multiply by 6 both sides to remove the fractions

4y=3x+48

Divide by 4 both sides

y=\frac{3}{4}x+\frac{48}{4}

Simplify

y=\frac{3}{4}x+12

The slope is

m_B=\frac{3}{4}

step 3

Compare the slopes

we have

m_A=\frac{3}{4}

m_B=\frac{3}{4}

so

m_A=m_B

therefore

The lines are parallel

see the attached figure to better understand the problem

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