Help me with matthhh
Help me with matthhh
Solution: A = 2 Please read the following step by step solution.
STEP 1: Read, understand the situation within, identify and pull out important information.
STEP 2: Translate keywords to their mathematical symbols:
STEP 3: Set up and solve the equation or problem:
y = (2/3)x - 6 Get rid of the variable x (with its coefficient) on the right side
-(2/3)x + y = -6 As "A" must be positive integer, get first rid of the denominator of the fraction coefficient of "x", by multiplying the whole equation by "3"
3 * ((-2/3) (x) + y = -6) Apply the distributive property of multiplication
(3/1)*(-2/3) (x) + 3y = 3*(-6)
(3*-2)/(1*3) (x) + 3y = -18 Simplify
-2x + 3y = -18 Now get rid of the negative sign of "x" by multiplying the whole equation by -1
(-1) (-2x + 3y = -18) Apply the distributive property of multiplication
2x - 3y = 18 There you have the equation in standard form! A = 2
STEP 4: Check the solution:
Transform the standard form equation solution into a slope intercept form. We must get the original equation given in slope intercept form!
2x - 3y = 18 Isolate "y" by first getting rid of 2x in the left side of the equation
-3y = -2x + 18 Get rid of the coefficient -3, by dividing the whole equation by -3
(-1/3) (-3y = -2x + 18) Applying the distributive property of multiplication
(3/3)y = (2/3)x + (-1/3) (18) Simplifying
y = (2/3)x -6 We got the same original slope intercept form equation!
STEP 5: Curiosities
y-intercept: 2(0)-3y=18; -3y=18; (-3/-3)y=(18)/(-3); y=-6;
y-intercept point (0, -6)
x-intercept: 2x-3(0)=18; 2x=18; (2/2)x=(18)/(2); x=9;
x-intercept point (9, 0)
Standard form of a linear equations is Ax + By = C.
y = 2/3x - 6
Multiply entire equation by 3 to remove the fraction.
3y = 2x - 18
Next, subtract 2x from both sides of the equation.
-2x + 3y = -18
Now we have the equation in standard form therefore the coefficient of the x-term is -2.
Note: There are infinite standard forms.
Standard form of a linear equation is Ax+By=C, where A, B, and C are all integers. Your equation is given in slope-intercept form (usually stated as y=mx+b), so we have to isolate the constant term and then multiply through by the least common denominator of any fractions in the coefficients.
y = (2/3)x + (-6)
(-2/3)x + y = (-6)
(-2)x + 3y = (-18)
And the coefficient of x is -2.