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3 years ago

Which equation is in slope intercept form and represents a line with the slope three through the point (9,-4)

Mathematics

1 answer:

beks73 [17]3 years ago

7 0

Answer:

y = 3x - 31

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3, thus

y = 3x + c ← is the partial equation

To find c substitute (9, - 4) into the partial equation

- 4 = 27 + c ⇒ c = - 4 - 27 = - 31

y = 3x - 31 ← equation in slope- intercept form

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elena-s [515]

ANSWER:

value of "a" is: a= -b√3+7+4√3

value of "b" is: $\frac{-a\sqrt{3}+7\sqrt{3} }{y} +4$

STEP-BY-STEP EXPLANATION:

<h2>how to get the value of "a":</h2><h2></h2>

1. (rationalize the denominator)

(2 + √3) × (2 + √3) =a + b√3

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + b√3

3. (use (a + b)² = a² + 2ab + b² to expand the expression)

4 + 4√3 + 3 = a + b√3

4. ( add the numbers)

7 + 4√3 = a + b√3

5. (move the variable to the left-hand side and change its sign. then, move the constants to the right-hand side and change their signs)

6. (change the signs on both sides of the equation)

a = -b√3 + 7 + 4√3

<h2>how to get the value of "b":</h2><h2></h2>

1. (rationalize the denominator. then, use the commutative property to reorder the terms)

(2 + $\sqrt{3}$ ) × (2 + $\sqrt{3}$ ) = a + b $\sqrt{3}$ → (2 +  $\sqrt{3}$ ) × (2 + $\sqrt{3}$  ) = a + $\sqrt{3}$ b

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + $\sqrt{3}$ b

3. (use (a + b)² = a² + 2ab + b² to expand the expression)

4 + 4 $\sqrt{3}$ + 3 = a + $\sqrt{3}$ b

4. (add the numbers)

7 + 4 $\sqrt{3}$ = a + $\sqrt{3}$ b

5. (move the expression to the left-hand side and change its sign. then, move the constants to the right-hand side and change their signs)

- $\sqrt{3}$ b + 7 + 4 $\sqrt{3}$ = a → - $\sqrt{3}$ b = a - 7 - 4 $\sqrt{3}$

6. (divide both sides of the equation by $-\sqrt{3}$ )

b = $- \frac{a}{\sqrt{3} } + \frac{7}{\sqrt{3}} + 4$

7. (rationalize the denominator)

b = $b=-\frac{a\sqrt{3} }{\s3}} +\frac{7\sqrt{3} }{{3} } +4$

8. (write all numerators above the common denominator)

b = $\frac{-a\sqrt{3}+7\sqrt{3} }{y} +4$

there you go! I hope this helped. goodluck! :)

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