Find the equation of the line

What is an equation of the line that passes through the point (- 1, - 3) and is perpendicular to the line x - 2y = 14 ?

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Perpendicular lines have slopes which are negative reciprocals.

To find the slope of the line x - 2y = 14, get it in slope-intercept form.

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

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   {slope-intercept 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 y-intercept is -5

y = mx + b   {slope-intercept 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

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