Answer:
The distance between the two parallel lines is y = -56·x - 1 and the parallel line that passes through the point (6, -4) is 5.91 units
Step-by-step explanation:
The parameters given are;
Equation of the line y = -56·x - 1
The point the parallel line passes = (6, -4)
Given that the slope and intercept form of a line is y = m·x + c
Where:
m = The slope = (y₂ - y₁)/(x₂ - x₁)
c = y- intercept
Comparing y = m·x + c with y = -56·x - 1 gives;
m = -56, c = -1
The equation of the parallel line is presented as follows
y - (-4) = (x - 6)(-56)
y = -56x +336 - 4 = -56x + 332
The formula for the distance, d, between two parallel lines is given by the following relation;
[tex]d = \dfrac{\left | c_1 - c_2\right |}{\sqrt{{a}^{2}+{b}^{2}} }[/tex]
Where:
c₁ and c₂ are the coordinates of the point constant y-intercept in both equations when the line equation is written as follows;
y = -56·x - 1 → y + 56·x + 1 = 0
a and b are the x and y coefficients
Which gives;
[tex]d = \dfrac{\left | 1 - 332\right |}{\sqrt{{56}^{2}+{1}^{2}} }[/tex] which gives [tex]d = \dfrac{331 \cdot \sqrt{3137} }{3137} = 5.91[/tex]
