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4 years ago

Write an equation of the line that passes through (-4,3) and (0,6). An equation is y =

Mathematics

1 answer:

VMariaS [17]4 years ago

3 0

Answer:

y= ¾x +6

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

Let's find the gradient first.

$gradient = \frac{y1 - y2}{x1 - x2}$

Using the formula above,

$m = \frac{6 - 3}{0 - ( - 4)} \\ m = \frac{3}{4}$

subst. the value of m into the equation.

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

To find c, substitute a coordinate.

When x=0, y=6,

$6 = \frac{3}{4} (0) + c \\ 6 = 0 + c \\ c = 6$

Thus, the equation of the line is $y = \frac{3}{4} x + 6$ .

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Graph the equation y=4x+1 by plotting points.

lidiya [134]

Look at the attached image (credit to Desmos graphing calculator)

To graph the equation y=4x+1, we just find two points that exist, plot them, and draw a straight line that goes through them.

Let's try x=0:

$y=4(0)+1=1$

One point on the line is (0,1)

Let's try x=1:

$y=4(1)+1=5$

Another point is (1,5).

Now, plot these two points and draw a line through them.

4 0

4 years ago

Read 2 more answers

Determine each of the following.

castortr0y [4]

Answer:

(a) $\{1,2,3,4,5,6,7,8,9,10\}$

(b) 10

(d) 0

(e) 1024

Step-by-step explanation:

(a)

A = {x ∈ Z | 0 < x, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

$0$ ... (1)

$x^2\leq 100$

Taking square root on both sides.

$-\sqrt{100}\leq x\leq \sqrt{100}$

$-10\leq x\leq 10$ .... (2)

Using (1) and (2) we get

$0$

Since x ∈ Z,

$A=\{1,2,3,4,5,6,7,8,9,10\}$

(b)

We need to find the value of | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.

$|A|=10$

| {x ∈ Z | 0 < x, x² ≤ 100}| = 10

(c)

B = {x ∈ Z | x > 10, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

$x>10$ ... (3)

$x^2\leq 100$

It means

$-10\leq x\leq 10$ .... (4)

Inequality (3) and (4) have no common solution, so B is null set or empty set.

$B=\{\}$

(d)

We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.

$|B|=0$

|{x ∈ Z | x > 10, x² ≤ 100}| = 0

(e)

We need to find the value of | P(A) |. P(A) is the power set of set A.

Number of elements of a power set is

$N=2^n$

where, n is the number of elements of set A.

We know that the number of elements of set is 10. So the value of |P(A)| is

$|P(A)|=2^{10}$

$|P(A)|=1024$

Therefore |P(A)|=1024.

7 0

3 years ago

X²+4x+20=0

andrezito [222]

Step-by-step explanation:

The general form of the quadratic equation is :

$ax^2+bx+c$

The given equation is x²+4x+20=0

On comparing the given equation and the general equation, we find that

a = 1, b = 4 and c = 20

Hence, the correct option is a=1 b =4 c = 20.

If the equation is 2x²+6x+5=0, then

a = 2, b = 6 and c = 5

If the equation is -2x²+x+5

a = -2, b = 1 and c = 5

7 0

3 years ago

How does probability apply to basketball?

andriy [413]

<span>depending on the player, a spectator can figure out the chance of the player making the basket ^_^</span>

3 0

4 years ago

One of the elephants in the zoo is on a special diet. Every day, the elephant eats the same amount of carrots that the rabbit ea

Naya [18.7K]

Answer:

1/3 kg.

Step-by-step explanation:

The ratio of the amount of carrots the elephant eats to the amount of carrots the rabbit eats in the same length of time is 365:1.

So if the total they both eat is 122 kg in one day, the rabbit eats 122 * 1/ 366

= 1/3 of a kg,

6 0

4 years ago