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3 years ago

what is the slope- intercept form of the equation of the line that passes through the points (-3,2) and(1,5)

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

6 0

Answer:

y = $\frac{3}{4}$ x + $\frac{17}{4}$

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 )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)

m = $\frac{5-2}{1+3}$ = $\frac{3}{4}$ , hence

y = $\frac{3}{4}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 5 ), then

5 = $\frac{3}{4}$ + c ⇒ c = 5 - $\frac{3}{4}$ = $\frac{17}{4}$

y = $\frac{3}{4}$ x + $\frac{17}{4}$ ← in slope-intercept form

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

Read 2 more answers

What is the inverse function of 15x + 14

Hitman42 [59]

The inverse fraction of 15x+14 is f^-1 (x)= x/15-14/15

3 0

3 years ago

Choose the best score on a quiz. 24 points out of 42 24 points out of 42 75 points out of 135 75 points out of 135 150 points ou

stellarik [79]

Answer:

150/250

Step-by-step explanation:

24/42, 75/135, 150/250, and 75/150 I believe is what you're asking. We know 75/135 is better than 75/150 so 75/150 is out of the equation. If we multiple 75/135 by 2 we get 150/270 which is more than 150/250, so 75/135 is out of the equation. Now to compare 24/42 and 150/250 we can divide their fractions, if we divide 24/42 we get 0.57, so 57%. If we did 150/250 we get 0.6 or 60%. So 150/250 is the best score.

8 0

2 years ago

Read 2 more answers

A coordinator will select 6 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different

g100num [7]

Answer:

84 different lineups are possible

Step-by-step explanation:

The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

6 musics from a set of 9. So

$C_{9,6} = \frac{9!}{6!(9-6)!} = 84$

84 different lineups are possible

4 0

3 years ago

during the 8-month shrimping season in the Gulf mexico, 325 shrimpers caught 4,913,977 pounds of shrimp and sold the shrimp $2 p

Hatshy [7]

STEP 1:
Find the $ total sold. Multiply total pounds by $2 sale price per pound.

=4,913,977 pounds * $2 a pound
=$9,827,954 total sold

STEP 2:
Divide the total sold above by the 325 shrimpers.

=$9,827,954 ÷ 325
=$30,239.858

Rounded to nearest dollar:
Each of the 325 shrimpers will take home $30,240.

Hope this helps! :)

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3 years ago