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Question 502883: slope 8/9, passing through (3,-1)
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! (3,-1)_m=(8)/(9)
Find the value of b using the formula for the equation of a line.
y=mx+b
Substitute the value of m into the equation.
y=((8)/(9))*x+b
Substitute the value of x into the equation.
y=((8)/(9))*(3)+b
Substitute the value of y into the equation.
(-1)=((8)/(9))*(3)+b
Since b is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
((8)/(9))*(3)+b=(-1)
Multiply ((8)/(9)) by (3) to get ((8)/(9))(3).
((8)/(9))(3)+b=(-1)
Remove the parentheses around the expression -1.
((8)/(9))(3)+b=-1
Multiply (8)/(9) by 3 to get (8)/(3).
((8)/(3))+b=-1
Remove the parentheses around the expression (8)/(3).
(8)/(3)+b=-1
Reorder the polynomial (8)/(3)+b alphabetically from left to right, starting with the highest order term.
b+(8)/(3)=-1
Since (8)/(3) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (8)/(3) from both sides.
b=-(8)/(3)-1
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
b=-1*(3)/(3)-(8)/(3)
Multiply -1 by 3 to get -3.
b=-(3)/(3)-(8)/(3)
Combine the numerators of all fractions that have common denominators.
b=(-3-8)/(3)
Subtract 8 from -3 to get -11.
b=(-11)/(3)
Move the minus sign from the numerator to the front of the expression.
b=-(11)/(3)
Now that the values of m(slope) and b(y-intercept) are known, substitute them into y=mx+b to find the equation of the line.
y=(8x)/(9)-(11)/(3)
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