What is the equation of the parallel line?

What is an equation of the line that passes through the point (−5,3) and is parallel to the line 3x − 5y = 30?

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Parallel lines have equal slopes. Find the slope of the given line, then use that same slope with the given point to find the equation of the line.

3x - 5y = 30 {given line}
-5y = -3x + 30 {subtracted 3x from each side}
y = (3/5)x - 6 {divided each side by -5}
slope = 3/5

The line parallel to that line also has a slope of 3/5.

Substitute the point and slope into slope-intercept form to get the y-intercept.

The point is (-5,3) and the slope is 3/5.
y = mx + b {slope-intercept form}
3 = (3/5)(-5) + b {substituted into slope-intercept form}
3 = -3 + b {multiplied}
b = 6 {added 3 to each side}

The slope is 3/5 and the y-intercept is 6.

y = (3/5)x + 6 is the equation of the line.

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