Answer :
The distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.
What is the equation of a line?
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The distance between the two straight parallel lines can be found by finding the difference between the y-intercept of the two lines. Therefore, for the two of the given equation, the value of the y-intercept can be written as,
Y-intercept of -4x + 7y + 9 = 0
-4x + 7y + 9 = 0
7y = 4x - 9
y = (4x - 9)/7
y = 4x/7 - 9/7
y-intercept = -9/7
Y-intercept of y = 4/7x - 9
y = 4/7x - 9
y-intercept = -9
Now, the difference distance between the two lines will be,
Distance = Difference between the y-intercept
= -9 - (-9/7)
= -9 + 1.2857
= 7.71
Hence, the distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.
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