Equation in standard form for the origin and (6,5)

Hello, Jaxon -

To develop the equation in standard form, it is necessary to (1) solve for the slope, m, in the Slope-Intercept form of the linear equation, and (2) using a given point, i.e., (6,5), to solve for "b", the y-intercept, as follows:

Utilize your "y=mx+b" slope-intercept form

[from the standard form of the linear equation in two unknowns (x,y), as in AX + BY = C]

Hence, solving for "m" first: m=(Y2-Y1)/(X2-X1) for X2,Y2) as (6,5) respectively, and through the Origin, (0,0) as (X1,Y1), and thusly, m=(5-0)/(6-0) = 5/6.

• So, now, with m=5/6, substitute (6,5) as (X,Y) in the general Y=mX+b to get

• 5= [(5/6) x 6] + b, and

• b= 0,

• So y=mX+ b simplifies to

• y=(5/6)X+ 0,

• and,

• Therefore, Y=(5/6)X, through the origin, where the y-intercept is b= 0.

•

Questions? Thanks for this opportunity: hope it arrives to help you in a timely manner, Jaxon: I would be glad to tutor you in your Algebra remotely.

Thanks again,

David / "Mr. Mac."

Wyzant Algebra Tutor

Wichita, KS 67213

To develop the equation in standard form, it is necessary to (1) solve for the slope, m, in the Slope-Intercept form of the linear equation, and (2) using a given point, i.e., (6,5), to solve for "b", the y-intercept, as follows:

Utilize your "y=mx+b" slope-intercept form

[from the standard form of the linear equation in two unknowns (x,y), as in AX + BY = C]

Hence, solving for "m" first: m=(Y2-Y1)/(X2-X1) for X2,Y2) as (6,5) respectively, and through the Origin, (0,0) as (X1,Y1), and thusly, m=(5-0)/(6-0) = 5/6.

• So, now, with m=5/6, substitute (6,5) as (X,Y) in the general Y=mX+b to get

• 5= [(5/6) x 6] + b, and

• b= 0,

• So y=mX+ b simplifies to

• y=(5/6)X+ 0,

• and,

• Therefore, Y=(5/6)X, through the origin, where the y-intercept is b= 0.

•

**Answer: 5X - 6Y = 0**where A=5, B = -6, and C = 0 in the Standard Form of the Straight Line (linear equation in two unknowns (X,Y).Questions? Thanks for this opportunity: hope it arrives to help you in a timely manner, Jaxon: I would be glad to tutor you in your Algebra remotely.

Thanks again,

David / "Mr. Mac."

Wyzant Algebra Tutor

Wichita, KS 67213