Create the equation of a line that is perpendicular to 2y = 14 + (2/3)x and passes through the point (-2,8).

**Perpendicular lines have slopes which are negative reciprocals.**

**Slope-intercept form is y = mx + b**

m is the slope

b is the y-intercept

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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