What is an equation of the line?

What is an equation of the line that passes through the point (-5,8) and is parallel to the line x + y = 8?

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Parallel lines have equal slopes.  Get the equation, x + y = 8, in slope-intercept form to identify the slope.

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

x + y = 8
y = -x + 8  {subtracted x from each side}
slope = -1 {the coefficient of x}

Use the slope of -1 and the point (-5,8) to get the equation of the new line.
Use slope-intercept form and substitute -5 in for x, 8 in for y, and -1 in for m, to find the y-intercept.

y = mx + b  {slope-intercept form}
8 = -1(-5) + b  {substituted}
8 = 5 + b  {multiplied}
b = 3  {subtracted 5 from each side}
y-intercept is 3

The slope is -1 and the y-intercept is 3.  Substitute back into slope-intercept form
to get the equation of the line.

y = -x + 3  {substituted}

Check with graphing calculator:

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