SOLUTION: 1) Write the equation y=1/3x - 2 in standard form using only integers and a positive coefficient for x. a) x+3y=6 b) x-3y=2 c)-x+3y=-6 d)x-3y=6 20 Which of the fol

Question 102658: 1) Write the equation y=1/3x - 2 in standard form using only integers and a positive coefficient for x.
a) x+3y=6 b) x-3y=2 c)-x+3y=-6 d)x-3y=6

20 Which of the following equations represents a line l that goes through (-1,-3) and has a slope of 4?
a)y=4x-3 b)y=4x+1 c)y=4x-1 d)y=4x+3

Please, can anyone help me with the above? thank you so much.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"1) Write the equation y=1/3x - 2 in standard form using only integers and a positive coefficient for x.
a) x+3y=6 b) x-3y=2 c)-x+3y=-6 d)x-3y=6 "

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)

Start with the given equation

Multiply both sides by the LCD 3

Distribute and multiply

Subtract 1x from both sides

Simplify

Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)

Distribute and simplify

The original equation (slope-intercept form) is equivalent to (standard form where A > 0)

The equation is in the form where , and

Now if you want A to be positive, multiply both sides by -1

Distribute and multiply

"
20 Which of the following equations represents a line l that goes through (-1,-3) and has a slope of 4?
a)y=4x-3 b)y=4x+1 c)y=4x-1 d)y=4x+3"

If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
where is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Rewrite as

Rewrite as

Distribute

Multiply and to get

Subtract 3 from both sides to isolate y

Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver )

Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
RELATED QUESTIONS
Write the equation y=1/3 x -2 in standard form using only integers and a positive... (answered by Alan3354)

Write the equation in standard form using only integers and a positive coefficient for... (answered by Alan3354)

write the equation of y = 1/3x - 2 in standard form using only integers and a positive... (answered by jim_thompson5910)

Write the equation y=2/3x-3 in standard form using only integers and a positive... (answered by user_dude2008)

How would you solve... Write the equation y + 1/4x-2 in standard form using only... (answered by Alan3354)

How would you solve... Write the equation y = 1/4x-2 in standard form using only... (answered by Alan3354)

Write the equation y = 4/3 x-1 in standard form using only integers and a positive... (answered by nerdybill)

write the equation y= (four-thirds)x-1 in the standard form using only integers and a... (answered by solver91311)

Please help I am lost. write the equation in standard form using only integers and... (answered by solver91311,mananth)