All categories

2 years ago

Write the slope-intercept form of the equation that passes through the point (-1, 2) and is parallel to the line y = 3/2x + 6

Mathematics

1 answer:

horsena [70]2 years ago

4 0

-------------------------------------------------------------------------------------------------------------

Answer: $\textsf{y = 3/2x + 7/2}$

-------------------------------------------------------------------------------------------------------------

Given: $\textsf{Passes through (-1, 2) and parallel to y = 3/2x + 6}$

Find: $\textsf{The equation in slope-intercept form}$

Solution: In order to determine the equation we know that our line is going to be parallel which means that the slope is the same and we need to use the point-slope form to help us. After plugging in the values we just simplify and solve for y to convert to slope-intercept form.

Plug in the values

$\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

$\textsf{y - 2 = 3/2(x - (-1))}$

Simplify and distribute

$\textsf{y - 2 = 3/2(x + 1)}$

$\textsf{y - 2 = (3/2 * x) + (3/2 * 1)}$

$\textsf{y - 2 = 3/2x + 3/2}$

Add 2 to both sides

$\textsf{y - 2 + 2 = 3/2x + 3/2 + 2}$

$\textsf{y = 3/2x + 3/2 + 2}$

$\textsf{y = 3/2x + 7/2}$

Therefore, after completing the steps we were able to determine that the equation that fits the description is y = 3/2x + 7/2.

You might be interested in

3x^2+5x-28=0 solve this for me please

jok3333 [9.3K]

Answer:

x= 7/3

x=-4

Step-by-step explanation:

Use the quadratic formula

a= 3, b=5, c=-28

-5± $\sqrt{5^2-4*3(-28)}$

x= _________________

2.3

Simplfy

$x=\frac{-5+19}{6} \\x=\frac{-5-19}{6}$

8 0

3 years ago

Given: △ABC, AB=5sqrt2 m∠A=45°, m∠C=30° Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

3 years ago

Let f(x)=5x+2 and gx=x^2-4x+1 <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bf%7D%7Bg%7D%285%29" id="TexFormula1" title="\f

Rasek [7]

Answer:

find f(5) and g(5) then divide f(5) by g(5) i.e f(5)/g(5) Answer will be 25/6

3 0

3 years ago

This figure consists of two semicircle and a rectangle

Maksim231197 [3]

The answer is C. 423.52 m

3 0

3 years ago

Read 2 more answers

Find the quotient 3^15/3^3

Sati [7]

There is a property called "Quotient of powers property", which states that:

$\frac{a^m}{a^n}=a^{(m-n)}$

Where "a" is the common base and "m" and "n" are exponents.

For this case, you have:

$\frac{3^{(15)}}{3^3}$

Then, in order to find the quotient, you must apply the Quotient of powers property. You need to write the common base (in this case is 3) and then subtract the exponents.

So, you get that the quotient is:

$\frac{3^{(15)}}{3^3}=3^{(15-3)}=3^{(12)}$

6 0

1 year ago