# Find the Slope and Y-Intercept (x-20)(x-10)+40+1/(3x)

(x-20)(x-10)+40+13x
Write (x-20)(x-10)+40+13x as an equation.
y=(x-20)(x-10)+40+13x
Rewrite in slope-intercept form.
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Simplify (x-20)(x-10)+40+13x.
Simplify each term.
Expand (x-20)(x-10) using the FOIL Method.
Apply the distributive property.
y=x(x-10)-20(x-10)+40+13x
Apply the distributive property.
y=x⋅x+x⋅-10-20(x-10)+40+13x
Apply the distributive property.
y=x⋅x+x⋅-10-20x-20⋅-10+40+13x
y=x⋅x+x⋅-10-20x-20⋅-10+40+13x
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
y=x2+x⋅-10-20x-20⋅-10+40+13x
Move -10 to the left of x.
y=x2-10⋅x-20x-20⋅-10+40+13x
Multiply -20 by -10.
y=x2-10x-20x+200+40+13x
y=x2-10x-20x+200+40+13x
Subtract 20x from -10x.
y=x2-30x+200+40+13x
y=x2-30x+200+40+13x
y=x2-30x+200+40+13x
y=x2-30x+240+13x
y=x2-30x+240+13x
Combine -30x+240+13x.
To write -30x as a fraction with a common denominator, multiply by 3x3x.
y=x2-30x⋅3x3x+13x+240
Simplify terms.
Combine -30x and 3x3x.
y=x2+-30x(3x)3x+13x+240
Combine the numerators over the common denominator.
y=x2+-30x(3x)+13x+240
y=x2+-30x(3x)+13x+240
Simplify the numerator.
Multiply x by x.
y=x2+-30⋅(3×2)+13x+240
Multiply -30 by 3.
y=x2+-90×2+13x+240
y=x2+-90×2+13x+240
To write 240 as a fraction with a common denominator, multiply by 3x3x.
y=x2+-90×2+13x+240⋅3x3x
Simplify terms.
Combine 240 and 3x3x.
y=x2+-90×2+13x+240(3x)3x
Combine the numerators over the common denominator.
y=x2+-90×2+1+240(3x)3x
y=x2+-90×2+1+240(3x)3x
Simplify the numerator.
Multiply 3 by 240.
y=x2+-90×2+1+720x3x
Reorder terms.
y=x2+-90×2+720x+13x
y=x2+-90×2+720x+13x
Simplify with factoring out.
Factor -1 out of -90×2.
y=x2+-(90×2)+720x+13x
Factor -1 out of 720x.
y=x2+-(90×2)-(-720x)+13x
Factor -1 out of -(90×2)-(-720x).
y=x2+-(90×2-720x)+13x
Rewrite 1 as -1(-1).
y=x2+-(90×2-720x)-1⋅-13x
Factor -1 out of -(90×2-720x)-1(-1).
y=x2+-(90×2-720x-1)3x
Simplify the expression.
Rewrite -(90×2-720x-1) as -1(90×2-720x-1).
y=x2+-1(90×2-720x-1)3x
Move the negative in front of the fraction.
y=x2-90×2-720x-13x
y=x2-90×2-720x-13x
y=x2-90×2-720x-13x
y=x2-90×2-720x-13x
y=x2-90×2-720x-13x
The equation is not linear, so the slope does not exist.
Not Linear
Find the Slope and Y-Intercept (x-20)(x-10)+40+1/(3x)