What is an equation of the line?

What is an equation of the line that passes through the point (1,3) and is parallel to the line 3x + y = 9?

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Parallel lines have equal slopes. Find the slope of the given line, and the new line will have the same slope.

Get the given equation in slope-intercept form, y = mx + b.
m is the slope and b is the y-intercept.

3x + y = 9 {given equation}
y = -3x + 9 {subtracted 3x from each side}
slope is -3 {the coefficient of x}

Substitute the slope, -3, along with the point, (1,3), into slope-intercept form, y = mx + b.

Point is (1,3) and slope is -3.
y = mx + b {slope-intercept form}
3 = -3(1) + b {substituted 1 in for x, 3 in for y, and -3 in for m}
3 = -3 + b {multiplied -3 by 1}
b = 6 {added 3 to each side}
y-intercept is 6

For the new line, slope is -3 and y-intercept is 6. Substitute those into slope-intercept form.

y = mx + b {slope-intercept form}
y = -3x + 6 {substituted -3 for m, the slope, and 6 for b, the y-intercept}

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