Answer:
The lines are perpendicular. Option B.
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:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The points are (3,4) and (7,3), thus the slope is:
[tex]\displaystyle m=\frac{3-4}{7-3}=-\frac{1}{4}[/tex]
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:
[tex]m1*m2=-1[/tex]
4*(-1/4)=-1
Both lines are perpendicular. Correct choice
D. Since choice B. is correct, this cannot be true. Incorrect