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Harrizon [31]
3 years ago
11

Write the slope-intercept form of the equation of each line given the slope and y-intercept.

Mathematics
1 answer:
saul85 [17]3 years ago
3 0

Answer:

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

2b. y + 2 = −⅔(x + 3)

2a. y - 3 = ⅘(x - 5)

1b. y = -x + 5

1a. y = 5x - 3

Step-by-step explanation:

4.

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

b.

2 = 6[1] + b

6

−4 = b

y = 6x - 4

-6x - 6x

_________

−6x + y = −4 >> Standard Equation

a.

4 = −7⁄4[-4] + b

7

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

____________

7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

__________________________________________________________

3.

Plug both coordinates into the Slope-Intercept Formula:

b.

5 = ½[4] + b

2

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

a.

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR <em>RATE OF CHANGES</em> [<em>SLOPES</em>].

__________________________________________________________

2.

b. y + 2 = −⅔(x + 3)

a. y - 3 = ⅘(x - 5)

According to the <em>Point-Slope Formula</em>, <em>y - y₁ = m(x - x₁)</em>, all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

__________________________________________________________

1.

b. y = -x + 5

a. y = 5x - 3

Just write out the Slope-Intercept Formula as it is given to you.

I am joyous to assist you anytime.

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Compare and contrast the results of adding or multiplying a value outside the argument of a function to the result of adding or
ki77a [65]

Answer:

Only in special funcitons, specifically linear functions whose graphs pass through the origin, it is the same to put the constant inside the argument or outside

Step-by-step explanation:

If the function has the form f(x) = a*x, where a is a constant, then we have that f(c*x) = a*(c*x) = c*(a*x) = c*f(x). This kind of functions are proportional to the identity function f(x) = x, and they comprehend the linear functions whose graph pass through the origin.

For other linear function this property isnt true. For example if f(x) = x+4, then

f(4) = 4+4 = 8,

f(2*4) = 8+4 = 12

2*f(4) = 2*8 = 16

Thus, 2*f(4) is not f(2*4).

This property also isnt true for quadratic functions for example. If f(x) = x², then f(1) = 1, thus 3*f(1) = 3, however, f(3*1) = 3² = 9.

There might be coincidences for specific values, for example if f(x) = (x-1)*(x-2), then f(2*1)=2*f(1) = 0, however, for any other constant the result is not the same (for example f(0*1) = (-1)*(-2)=2, and 0*f(1) = 0).

If we want a function to satisfy the property f(c*x) = c*f(x) for any c,x, then it should be true that f(c) = f(c*1) = c*f(1). This means that if f(1) = a, then f(c) = c*a, so, in other words, f(x) = a*x = f(1) * x.

5 0
3 years ago
What are the coordinates of the new triangle
swat32
All you need to do is subtract.
1-5 is -4. 1-3 is -2 thus (-4,-2)
4-5=-1. 2-3=-1 thus (-1,-1) at this point there is only one option left
B Is the answer
6 0
3 years ago
Lines k and n are perpendicular.if the slope of line k is -6,what is the slope of line n?
aleksley [76]

Answer:

1/6

Step-by-step explanation:

Well perpendicular lines are reciprocals of each other,

meaning if like k has a slope of -6 then line n will have a slope of positive 1/6.

<em>Thus,</em>

<em>line n has a slope of 1/6.</em>

<em />

<em>Hope this helps:)</em>

3 0
3 years ago
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The perimeter of an equilateral triangle is 63 inches. If the length pf each side is (4x-3), write an equation and find the valu
Nady [450]

Answer:

x = 6

Step-by-step explanation:

Givens

There are 3 sides. All are equal to (4x - 3)

Their sum = 63

Formula

3(4x - 3) = 63

Solution

  • 3(4x - 3) = 63            Divide by 3
  • 12x - 9 = 63               Add 9 to both sides
  • 12x = 63 + 9    
  • 12x = 72                    Divide by 12
  • x = 72/12

x = 6                          Answer  

7 0
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