Which equation represents the line that is perpendicular to graph of 4x+3y=9 and passes through (-2,3)

The equation that represents the line that is perpendicular to 4x+3y=9 and passes through the point, (-2,3) is:

Recall:

First, rewrite 4x+3y=9 in slope-intercept form to find the slope.

4x+3y=9

3y = -4x + 9

y = -4/3x + 3

The slope of 4x+3y=9 is -4/3.

The line that is perpendicular to 4x+3y=9 will have a slope of 3/4 (negative reciprocal of -4/3).

To write the equation of the line that is perpendicular to 4x+3y=9  and passes through the point, (-2,3), substitute (a, b) = (-2,3) and m = 3/4 into y - b = m(x - a):

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

y - 3 = 3/4(x + 2) (point-slope form)

y - 3 = 3/4x + 3/2

y = 3/4x + 3/2 + 3

y = 3/4x + 9/2 (slope-intercept form)

The equation that represents the line that is perpendicular to 4x+3y=9 and passes through the point, (-2,3) is:

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