What is the acute angle between the lines 3x - 2y = 9 and x + y = 8

Expert Answers

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If a line has a slope of m and the angle it makes with the x-axis is `theta, m = tan theta`.

Write the equations of the lines in the form y = mx + c, where m is their slope.

3x - 2y = 9

=> 2y = 3x - 9

=> y = (3/2)x - 9

The slope of the line is (3/2).

x + y = 8

=> y = -x + 8

The slope is -1.

For two lines with slopes m1 and m2. and if the acute angle between them is `phi, tan phi = (m2 - m1)/(1 - m2*m1)` ,

Substituting the values we have,

=> `tan phi = ((3/2) + 1)/(1 + (3/2))`

=> `tan phi = 1`

=> `phi = tan^-1 (1)`

=> `phi = 45` degrees

The acute angle between lines is 45 degrees.

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