What is an equation of the line?

​What is an equation of the line that passes through the point (-8,0) and is parallel to the line x + 2y = 14?

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Parallel lines have equal slopes.  Get the equation in slope-intercept form, so that you can identify the slope of the line.  Then, use that slope with the given point to get the equation of the line.

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

x + 2y = 14  {the given equation}
2y = -x + 14  {subtracted x from each side}
y = (-1/2)x + 7   {divided each side by 2}
slope = -1/2

(-8,0) and m = -1/2 are the point and the slope.  Substitute into slope-intercept form to get the y-intercept.

y = mx + b   {slope-intercept form}
0 = (-1/2)(-8) + b   {substituted the point and slope into slope-intercept form}
0 = 4 + b   {multiplied}
b = -4   {subtracted 4 from each side}
y-intercept = -4

Substitute the slope, -1/2, and the y-intercept, -4, back into slope-intercept form.

y = mx + b   {slope-intercept form}
y = (-1/2)x - 4 is the equation of the line.

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