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3 years ago

If a line passes through the points (-5,-4) and (3,-1), the equation of the line is?

Mathematics

2 answers:

Morgarella [4.7K]3 years ago

6 0

y = $\frac{3}{8}$ x - $\frac{17}{8}$

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 ) = (- 5, - 4 ) and (x₂, y₂ ) = (3 , - 1 )

m = $\frac{-1+4}{3+5}$ = $\frac{3}{8}$

the partial equation is y = $\frac{3}{8}$ x + c

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

using (3, - 1 ), then

- 1 = $\frac{9}{8}$ + c ⇒ c = - $\frac{17}{8}$

y = $\frac{3}{8}$ x - $\frac{17}{8}$ ← in slope-intercept form

Ratling [72]3 years ago

3 0

answer: y = 1.5x - 5.5

explanation:

use y = mx +b to model your equation

(m = slope, b = y-intercept)

let's start by finding slope

to find slope, subtract the y values over the x values.

- 4 - (-1) / - 5 - (-3)

solve and simplify.

-3 / -2

two negatives equals a positive, so convert into a decimal and remove the negative

you get 1.5.

now, plug the slope a y and x value into the equation to find b, the missing value.

-1 = 1.5(3) + b

-1 = 4.5 + b

-5.5= b

so, your equation is y = 1.5x - 5.5.

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Car dealerships claim to make most of their money from servicing cars. In a certain month, an Acura dealership sold fifteen less

MA_775_DIABLO [31]

Answer:

New cars sold = 20,

Used cars sold = 25

Cars serviced = 290

Step-by-step explanation:

In a month they sold fifteen less used cars than twice the number of new cars.

Lets say 'x' number of new cars were sold, then:

The number of used car sold is:

$2\times x-15=2x-15$

In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:

$12\times x+50=12x+50$

Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:

$x+(2x-15)+(12x+15)=335$

Solving for 'x' we get:

$x+2x+12x-15+50=335$

$15x+35=335$

$15x=335-35=300$

$x=\frac{300}{15}=20$

Therefore, the number of new cars sold in that month is 20.

Number of used car sold $=2x-15=2\times 20-15=40-15=25$

Number of cars serviced $=12\times x+50=12\times20+50=240+50=290$

We can also cross check by summing them up:

$290+25+20=335$

8 0

3 years ago

Find the x-value for point C such that AC and BC from a 2:3 ratio.

Galina-37 [17]

Given:

Point C divides AB such that AC:BC=2:3.

To find:

The x-value for point C.

Solution:

Section formula: If a point divide a line segment in m:n, then

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Form the given graph it is clear that the endpoints of the line segment AB are A(-3,5) and B(3,0).

Point C divides AB such that AC:BC=2:3. Using section formula, the coordinates of point C are

$C=\left(\dfrac{2(3)+3(-3)}{2+3},\dfrac{2(0)+3(5)}{2+3}\right)$

$C=\left(\dfrac{6-9}{5},\dfrac{0+15}{5}\right)$

$C=\left(\dfrac{-3}{5},\dfrac{15}{5}\right)$

$C=\left(-0.6,3\right)$

The x-value of C is -0.6.

Therefore, the correct option is B.

6 0

3 years ago

Find the equation of a parabola with a vertical axis and its vertex at the origin and passing through the point (-2, 3).

jonny [76]

Answer:

$y=\frac{3}{4}x^2$

Step-by-step explanation:

Hi there!

Because we're given the vertex of the parabola, we can determine its equation in vertex form:

$y=a(x-h)^2+k$ where the vertex is $(h,k)$

Plug in the vertex (0,0)

$y=a(x-0)^2+0\\y=a(x)^2\\y=a(x-0)^2+0\\y=ax^2$

Now, we must solve for a. Plug in the given point (-2,3) and solve for a:

$3=a(-2)^2\\3=4a\\\frac{3}{4} =a$

Therefore, the value of a is $\frac{3}{4}$ . Plug this back into $y=ax^2$ :

$y=\frac{3}{4}x^2$

I hope this helps!

5 0

3 years ago

In a survey of milk drinkers,24 out of 40 milk drinkers said they preferred chocolate milk.If 600 milk drinkers are surveyed,how

kolbaska11 [484]

24/40 = 360/600
360 will prefer chocolate milk.

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4 years ago

Read 2 more answers

Hi pls help I need helppp

Readme [11.4K]

Answer:

Step-by-step explanation:

Ben is buying 30 juice boxes. Since each pack has 3 juice boxes, we can make it (30 / 3) so far. 30 / 3 is how many packs Ben buys. Now, since each pack is $1.25, we have to multiply 30 / 3 by 1.25.

Therefore, the answer is c = (30 / 3) * 1.25

I hope this helped and please mark me as brainliest!

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3 years ago