What is an equation of the line that passes through the point (1,3) and is parallel to the line 3x + y = 9?
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 slopeintercept form, y = mx + b. m is the slope and b is the yintercept. 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 slopeintercept form, y = mx + b. Point is (1,3) and slope is 3. y = mx + b {slopeintercept 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} yintercept is 6 For the new line, slope is 3 and yintercept is 6. Substitute those into slopeintercept form. y = mx + b {slopeintercept form} y = 3x + 6 {substituted 3 for m, the slope, and 6 for b, the yintercept} Ask Algebra House
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