What is an equation of the line that passes through the point ( 1,  3) and is perpendicular to the line x  2y = 14 ?
Perpendicular lines have slopes which are negative reciprocals.
To find the slope of the line x  2y = 14, get it in slopeintercept form. Slopeintercept form is y = mx + b m is the slope b is the yintercept x  2y = 14 2y = x + 14 {subtracted x from each side} y = (1/2)x  7 {divided each side by 2} slope = 1/2 The perpendicular slope would be 2. Using the point (1,3) and the slope 2, get the equation of the line. y = mx + b {slopeintercept form} 3 = (2)(1) + b {substituted 3 for y, 2 for m, and 1 for x} 3 = 2 + b {multiplied 2 by 1} b = 5 {subtracted 2 from each side} On the new line, the slope is 2 and the yintercept is 5 y = mx + b {slopeintercept form, once again} y = 2x  5 {substituted 2 for m and 5 for b} The equation of the line passing through (1,3) and perpendicular to x  2y = 14 is: y = 2x  5 Ask the House
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