What is an equation of the line that passes through the point (−5,3) and is parallel to the line 3x − 5y = 30?
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 slopeintercept form to get the yintercept. The point is (5,3) and the slope is 3/5. y = mx + b {slopeintercept form} 3 = (3/5)(5) + b {substituted into slopeintercept form} 3 = 3 + b {multiplied} b = 6 {added 3 to each side} The slope is 3/5 and the yintercept is 6. y = (3/5)x + 6 is the equation of the line. Ask Algebra House
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