Find the equation of the line

Create the equation of a line that is perpendicular to 2y = 14 + (2/3)x and passes through the point (-2,8).
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Perpendicular lines have slopes which are negative reciprocals.

Slope-intercept form is y = mx + b
m is the slope 
b is the y-intercept

Find the slope of the given line, then take the negative reciprocal to get the slope of the new line.
 2y = 14 + (2/3)x
y = (1/3)x + 7   {divided each side by 2 and re-arranged to be in slope-intercept form}
slope = 1/3   {slope is the number in front of the x, when in slope-intercept form}

Perpendicular slope = -3   {took negative reciprocal of 1/3}

Use slope intercept form to get the equation of the line with a slope of -3 and passing through (-2,8).

slope is -3 and point is (-2,8)
y = mx + b   {slope-intercept form}
8 = -3(-2) + b   {substituted point and slope into slope-intercept form}
8 = 6 + b   {multiplied}
b = 2   {subtracted 2/3 from each side}

y = -3x + 2   {substituted slope and y-intercept into slope-intercept form}

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