Question

Can you help me with this true and false problem?

Answer 1

Answers:

FALSE.

Explanations:

Given the linear relations 2x - 3y = 4 and y = -2/3 x + 5

Both equations are equations of a line. For the lines to be perpendicular, the product of their slope is -1

The standard equation of a line in slope-intercept form is expressed as

`y=mx+b`

m is the slope of the line

For the line 2x - 3y = 4, rewrite in standard form

`\begin{gathered} 2x-3y=4 \\ -3y=-2x+4 \\ y=(-2)/(-3)x-(4)/(3) \\ y=(2)/(3)x-(4)/(3) \end{gathered}`

Compare with the general equation

`\begin{gathered} mx=(2)/(3)x \\ m=(2)/(3) \end{gathered}`

The slope of the line 2x - 3y = 4 is 2/3

For the line y = -2/3 x + 5

`\begin{gathered} mx=-(2)/(3)x \\ m=-(2)/(3) \end{gathered}`

The slope of the line y = -2/3 x + 5 is -2/3

Take the product of their slope to determine whether they are perpendicular

`\begin{gathered} \text{Product = }(2)/(3)*-(2)/(3) \\ \text{Product = -}(4)/(9) \end{gathered}`

Since the product of their slope is not -1, hence the linear relations do not represent lines that are perpendicular. Hence the correct answer is FALSE