Answer:
Therefore, we conclude that correct answer is: The slope is [tex]-\frac{3}{2}[/tex] and contains the point [tex](0, -2)[/tex].
Step-by-step explanation:
From Analytical Geometry we remember that slopes of two lines that are perpendicular to each other observe the following relationship:
[tex]m_{\perp} = -\frac{1}{m}[/tex] (Eq. 1)
Where:
[tex]m[/tex] - Slope of the original line, dimensionless.
[tex]m_{\perp}[/tex] - Slope of the perpendicular line, dimensionless.
At first we must determine the slope of original line by definition of secant line:
[tex]m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (Eq. 2)
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Initial and final independent variables, dimensionless.
[tex]y_{A}[/tex], [tex]y_{B}[/tex] - Initial and final dependent variables, dimensionless.
If we know that [tex]A(x,y) = (-3,-4)[/tex] and [tex]B(x,y) = (3,0)[/tex], the slope of original line is:
[tex]m = \frac{0-(-4)}{3-(-3)}[/tex]
[tex]m = \frac{2}{3}[/tex]
In addition, the standard form of original line is represented by this formula:
[tex]y = m\cdot x +b[/tex] (Eq. 3)
Where [tex]b[/tex] is the y-Intercept of original line, dimensionless.
If we get that [tex]m = \frac{2}{3}[/tex], [tex]x =3[/tex], [tex]y = 0[/tex], then y-Intercept of the line is:
[tex]b = y-m\cdot x[/tex]
[tex]b = 0-\left(\frac{2}{3} \right)\cdot (3)[/tex]
[tex]b = -2[/tex]
From (Eq. 1) we get that slope of perpendicular line is:
[tex]m_{\perp} = -\frac{1}{\frac{2}{3} }[/tex]
[tex]m_{\perp} = - \frac{3}{2}[/tex]
The slope of perpendicular line is [tex]-\frac{3}{2}[/tex].
And we procced to use the equation of perpendicular line in standard form is:
[tex]y = m_{\perp}\cdot x +b[/tex] (Eq. 4)
If we know that [tex]m_{\perp} = - \frac{3}{2}[/tex], [tex]b = -2[/tex] and [tex]x = 0[/tex], the value of [tex]y[/tex] is:
[tex]y = \left(-\frac{3}{2}\right)\cdot (0)-2[/tex]
[tex]y = -2[/tex]
Therefore, we conclude that correct answer is: The slope is [tex]-\frac{3}{2}[/tex] and contains the point [tex](0, -2)[/tex].
Answer:
The slope is Negative three-halves and contains the point (0, −2).
Step-by-step explanation:
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