Find an equation of the line that passes through the point (2, 3) and is perpendicular to the line 4x - 3y = 10.

Solution:

Given, the equation is 4x - 3y = 10

We have to find an equation of the line that passes through the point (2, 3).

The equation of the line in slope-intercept form is given by

y = mx + c --- (1)

Converting the given equation to slope-intercept form,

4x - 10 = 3y

y = (4/3)x - 10/3 --- (2)

Comparing (1) and (2),

Slope, m = 4/3

Since, the line is perpendicular to the given line,

Slope = -1/m

Slope = -3/4

At (2, 3),

3 = (-3/4)(2) + c

3 = (-3/2) + c

3 + 3/2 = c

c = 9/2

The equation of the line is y = (-3/4)x + 9/2.

Therefore, the equation of the line is y = (-3/4)x + 9/2.

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Find an equation of the line that passes through the point (2, 3) and is perpendicular to the line 4x - 3y = 10.

Summary:

An equation of the line that passes through the point (2, 3) and is perpendicular to the line 4x - 3y = 10 is y = (-3/4)x + 9/2.