Answer:the answer is B. If you graph all 4 answers, y=1/3x + 4 is the only answer that is perpendicular
Step-by-step explanation:
Equation y = 1/3 x + 4 represents a line that is perpendicular to line PQ. Option B is correct.
The equation that represents a line that is perpendicular to the line PQ is to be chosen from the options.
A line can be defined by the shortest distance between two points is called a line. Equation of line is given by [tex]y = mx +c[/tex] where m is the slope of the line and c is constant.
The slope of line PQ = [tex]m_1[/tex]
The slope of the line perpendicular to the line PQ given by,
[tex]m_1* m_2=-1[/tex]
[tex]m_1 = \frac{y_2-y_1}{x_2-x_1}[/tex]
where coordinates, (x, y) are (-8, 7) and (-4, -5).
[tex]m_1 =\frac{7+5}{-8+4}[/tex]
[tex]m_1[/tex] = 12/-4
[tex]m_1[/tex] = 3
Now slope [tex]m_2[/tex]
[tex]m_1* m_2=-1\\-3* m_2=-1\\m_2=1/3[/tex]
While comparing the slope of the equation only the equation y = 1/3 x + 4
has a slope of m = 1/3.
Thus. equation y = 1/3 x + 4 represents a line that is perpendicular to line PQ. Option B is correct.
Learn more about lines here:
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