What is the equation of the line that passes through (1/2, -1/2) and (1/9, 3/9)?
I keep on messing up w/ the complex fractions.
Would you like to post your work?
ok
slope: (-9/18 - 6/18)/
9/18-2/18
=(-15/18)/ (7/18)
this is where i get stuck
how do i simplify these so i can substitute them into slope intercept form
(-15/18) / (7/18) = (-15/18) * (18/7)
To find the equation of a line passing through two points, you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points and m is the slope of the line.
First, let's calculate the slope (m) using the two points (1/2, -1/2) and (1/9, 3/9):
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates:
m = ((3/9) - (-1/2)) / ((1/9) - (1/2))
To simplify the fractions, remember you can convert the mixed numbers (whole number + fraction) to improper fractions. For example, -1/2 can be written as -3/6, and 3/9 as 1/3.
m = ((1/3) - (-3/6)) / ((1/9) - (1/2))
= (1/3 + 3/6) / (1/9 - 1/2)
= (1/3 + 1/2) / (1/9 - 4/9)
= (2/6 + 3/6) / (-3/9)
= 5/6 / -3/9
= 5/6 * (-9/3)
= -5/2
Now that we have the slope (m = -5/2) and one point (1/2, -1/2), we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
y - (-1/2) = -(5/2)(x - 1/2)
Next, we can simplify the right side of the equation:
y + 1/2 = -(5/2)(x - 1/2)
y + 1/2 = (-5/2)x + (5/4)
y = (-5/2)x + (5/4) - (1/2)
y = (-5/2)x + (5/4) - (2/4)
y = (-5/2)x + (3/4)
Therefore, the equation of the line passing through (1/2, -1/2) and (1/9, 3/9) is y = (-5/2)x + (3/4).