equation in slope...?

Question

Write an equation in slope-intercept form of the like that passes through the given point and it parrallel to th graph of each equation.

(5,-4), x - 3y = 8

if someone could maybe help me solve this?

Answer 1

the slope of the line perpendicular to that line would be the inverse negative of the slope of x-3y = 8

(x-8)/3 = y

the slope = x/3, so the perpendicular line has a slope of -3x

y = mx + b

m = -3

x = 5

y = -4

-4 = -15 + b

b = 11

y = -3x + 11

Answer 2

First solve for the slope of the first line
because a parallel line has the same slope
1x - 3y = 8 (the 1 in front of the x is handy to note)
-3y = -1x + 8
y = (-1/-3)x + 8/-3
y = 1/3x - 8/3
m = slope = 1/3
new equation
y = mx + b
y = -4 and x = 5
Now solve for b, we now know m = 1/3
y = -4 = 1/3(5) + b
solve for b... -4 - 5/3 = b = -17/3
new equation y = 1/3x - 17/3

Answer 3

Line thru (5,-4) is
y - (-4) = m(x - 5) You know this standard equation?

Parallel to x - 3y = 8 means the gradient (m) must be equal to the gradient of this line. If you add 3y to both sides of this equation, then take 8 from both sides, and then divide both sides by 3 you get
x/3 - 8/3 = y
Now x/3 is the same as (x/1)*(1/3) and so the gradient is 1/3. Put this into the equation I wrote at the top:

y + 4 = (1/3)*(x - 5)
Remove parentheses on the righthand side and then add -4 to both sides and you have the answer.

Answer 4

If your new line is parallel to the original line, that means it will have the same slope. So, first off you need to put your original line in standard y=mx+b format:

x - 3y = 8
3y = x - 8
y = 1/3 x - 8/3

So m = 1/3 is the slope for your original line and the slope for your new line.

So our new line is y = 1/3 x + b, but we still need to solve for b.

Since we know one point in our new line, we can plug that in for x,y in our new line's equation to solve for b:

y = 1/3 x + b
b = y - 1/3 x
b = -4 - 1/3(5)
b = -4 - 5/3 = -12/3 - 5/3 = -17/3

So the equation of our new line is as follows:

y = 1/3 x - 17/3

Hope that helped!

~ ♥ ~

Answer 5

the equations of yours:

y=1/3x-8/3

so, the slope os 1/3 and it is the same for all parallels

so, the equation for any parallel is: y=1/3x-b
putting y=-4
x=5

-4=5/3-b

so, b= 5/3+4=5 2/3

so, the equation is: y=1/3+5 2/3

Answer 6

Slope intercept for is: y = mx + b for the reason which you have all the values different than b you could fill in and remedy for b. y = mx + b -5 = (4/5)(0) + b -5 = 0 + b b = -5 So, y = (4/5)x - 5

Answer 7

x - 3y = 8
So y = ⅓x - 8/3
Slope = ⅓

Equation of new line of form y = ⅓x + b
When x = 5; y = -4
So - 4 = ⅓*5 + b
b = -17/3
So required line is y = ⅓x - 17/3
-----------------
OR Method 2
-----------------
x - 3y = 8
Parallel line of form x - 3y = k
When x = 5 y = -4
so 5 - 3 * -4 = k
So k = 17
Thus required line is
x - 3y = 17 (ie y = ⅓x - 17/3)

Answer 8

(5,-4)
x - 3y = 8
-3y=-x+8
y=x/3-8/3

m=1/3

y=x/3+b
-4=5/3+b
b=-4-5/3=-12/3-5/3=-17/3

y=x/3-17/3

Answer 9

x-3y=8

-3y=-x+8

-3(-4)=-1(5)+8

12=-5x+8

good luck