y= 2/3X-6

Help me with matthhh

y= 2/3X-6

Help me with matthhh

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**Solution: A = 2** Please read the following step by step solution.

STEP 1: **Read**, **understand** the situation within,
**identify** and pull out **important** information.

- y = (2/3)x - 6 it's in a slope form equation y=mx+b, where m(slope)=2/3; b(y-intercept)=-6
- The standard form equation leads to the slope form equation just by isolating "y" and by doing opposite operations.
- To transform a "slope form" into a "standard form", we just do the inverse process: the variables x, y, must be in the same side of the equation.

STEP 2: **Translate keywords** to their mathematical symbols:

- Standard form equation: Ax + By = C, where A is a positive integer, B and C integer numbers
- A = ? ; B = ? ; C = ?

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 -(2/3)x

-(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

-2x -2x

-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**

- Having the equation in "standard form" it's really easy to get the
**y-intercept point**(0,y) and the**x-intercept point**(x,0).

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)*

**Graphing**the equation in standard form: find the y-intercept point and x-intercept point, as we already did it. Plot them in a Cartesian plane and draw a line through both intercept points. And voila' you got it!

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.

Philip N. | Certified 5-12 Math TeacherCertified 5-12 Math Teacher

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.

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