Find the distance between y=−56x−1 and the parallel line that passes through (6,−4). Round your answer to the nearest tenth.

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;

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;

which gives

1gm = 1000mg so 0.1gm = 1000mg

first, convert the weight to kg

160lb * 1kg/2.2lb = 72.7kg

next, the dose

72.7kg * 100mg/kg = 7270mg

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c