Answer:
[tex]n = 304[/tex]
Step-by-step explanation:
Given
[tex]y = -15x - 6[/tex]
[tex]Points: (n,-12) \& (4,8)[/tex]
Required
Determine the value of n
First, we need to determine the slope of the given equation.
An equation is of the form;
[tex]y = m_1x + b[/tex]
Where m = slope.
By comparison.
[tex]m_1 = -15[/tex]
Since the given point and the given equation are perpendicular, then:
[tex]m = -\frac{1}{m_1}[/tex]
[tex]m = -\frac{1}{-15}[/tex]
[tex]m = \frac{1}{15}[/tex]
The slope of the point is calculated as thus:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (n,-12)[/tex]
[tex](x_2,y_2) = (4,8)[/tex]
[tex]m = \frac{1}{15}[/tex]
So, we have:
[tex]\frac{1}{15} = \frac{8 - (-12)}{4 - n}[/tex]
[tex]\frac{1}{15} = \frac{8 +12}{4 - n}[/tex]
[tex]\frac{1}{15} = \frac{20}{4 - n}[/tex]
Cross Multiply
[tex]4 - n = 20 * 15[/tex]
[tex]4 - n = 300[/tex]
Solve for n
[tex]n = 4 + 300[/tex]
[tex]n = 304[/tex]
