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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (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)


y+=+%281%2F3%29x-2 Start with the given equation


3%2Ay+=+3%2A%28%281%2F3%29x-2%29 Multiply both sides by the LCD 3


3y+=+1x-6 Distribute and multiply


3y-1x+=+1x-6-1x Subtract 1x from both sides


-1x%2B3y+=+-6 Simplify


-1%2A%28-1x%2B3y%29+=+-1%2A%28-6%29 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)


1x-3y+=+6 Distribute and simplify


The original equation y+=+%281%2F3%29x-2 (slope-intercept form) is equivalent to 1x-3y+=+6 (standard form where A > 0)


The equation 1x-3y+=+6 is in the form Ax%2BBy+=+C where A+=+1, B+=+-3 and C+=+6





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


-1%28-x%2B3y%29=-1%28-6%29


x-3y=6 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 4 which goes through the point (-1,-3), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

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

y--3=%284%29%28x--1%29 Plug in m=4, x%5B1%5D=-1, and y%5B1%5D=-3 (these values are given)


y%2B3=%284%29%28x--1%29 Rewrite y--3 as y%2B3


y%2B3=%284%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B3=4x%2B%284%29%281%29 Distribute 4

y%2B3=4x%2B4 Multiply 4 and 1 to get 4

y=4x%2B4-3 Subtract 3 from both sides to isolate y

y=4x%2B1 Combine like terms 4 and -3 to get 1
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Answer:


So the equation of the line with a slope of 4 which goes through the point (-1,-3) is:

y=4x%2B1 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=1

Notice if we graph the equation y=4x%2B1 and plot the point (-1,-3), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x%2B1 through the point (-1,-3)
and we can see that the point lies on the line. Since we know the equation has a slope of 4 and goes through the point (-1,-3), this verifies our answer.