Question

Y = 4x - 5 and (3,4) (7, 3) A. parallel B. perpendicular D. neither

Answer 1

The lines are perpendicular. Option B.

Step-by-step explanation:

Equation of the Line

One of the characteristics of the line is its slope. It can be determined in two ways:

* From the equation y=mx+b, the m is the slope. The given equation is y=4x-5. Thus, the slope of this line is m=4.

* Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

The points are (3,4) and (7,3), thus the slope is:

`\displaystyle m=(3-4)/(7-3)=-(1)/(4)`

A. For two lines to be parallel, their slopes must be equal. Since m1=4 and m2=-1/4, the lines are not parallel. Incorrect

B. For two lines to be perpendicular, their slopes must meet the condition:

`m1*m2=-1`

4*(-1/4)=-1

Both lines are perpendicular. Correct choice

D. Since choice B. is correct, this cannot be true. Incorrect