Question 358479
Which is the equation of a line parallel to a line containing the points (-3, 1) and (6, 4) and passing throught the point (5, 2)?


slope-intercept form of a line is y = mx + b
where m is the slope,
and b is the y-intercept (vertical-intercept, or point (0,b))


m = slope = rise/run = (y2 - y1)/(x2 - x1)
m = (4 - 1)/(6 - -3) = 3/(6 + 3) = 3/9 = 1/3
parallel lines have the same slope


y = (1/3)x + b, solve for b by plugging in point (5,2)
2 = (1/3)(5) + b
2 = 5/3 + b
2 - 5/3 = b
1/3 = b (2 = 6/3)
y = (1/3)x + 1/3 (equation of line containing (5,2))


equation of line containing (-3,1):
1 = (1/3)(-3) + b
1 = -1 + b
2 = b
y = (1/3)x + 2


equation of line containing (6,4) will also be y = (1/3)x + 2:
4 = (1/3)(6) + b
4 = 6/3 + b
4 = 2 + b
2 = b
y = (1/3)x + 2