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4 years ago

Which equation represents the line shown?

Mathematics

1 answer:

aleksandrvk [35]4 years ago

4 0

Answer:

the first option

Step-by-step explanation:

okay so the line passes through the 2 on the y-axis making it the y-intercept

that means you can eliminate the second and third options

now to find the slope, you can use rise over run (y2-y1/x2-x1)

3-2/3-0 = 1/3

so the slope is 1/3

all together, the equation would be:

f(x) = 1/3x + 2

so the answer is the first option

You might be interested in

Select the correct steps for factoring the polynomial 5x^3-40

erastovalidia [21]

Answer:

5 (x-2) (x²+2x+4)

Step-by-step explanation:

Stating with 5x³ - 40, the want to simplify the x part by extracting the common factor, so

5x³ - 40 = 5(x³-8)

Now to factor x³-8, we can rewrite it in the format x³-2³, right?

And there's a formula to obtain x³-y³, which is the Difference of Cubes formula that goes like this: x³-y³= (x-y)(x²+xy+y²)

So, we apply this formula replacing the y with our value of 2:

x³-2³= (x-2)(x²+2x+2²) = (x-2)(x²+2x+4)

So, overall, we have 5x³ - 40 = 5 (x-2) (x²+2x+4)

7 0

3 years ago

Write the equation of the parabola that has its x-intercepts at (1+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B5%7D" id="TexForm

VladimirAG [237]

Answer:

$y=2x^2-4x-8$

Step-by-step explanation:

<u>Factored form of a parabola</u>

$y=a(x-p)(x-q)$

where:

p and q are the x-intercepts.
a is some constant.

Given x-intercepts:

(1+√5, 0)
(1-√5, 0)

Therefore:

$\implies y=a(x-(1+\sqrt{5}))(x-(1-\sqrt{5}))$

$\implies y=a(x-1-\sqrt{5})(x-1+\sqrt{5})$

To find a, substitute the given point (4, 8) into the equation and solve for a:

$\implies a(4-1-\sqrt{5})(4-1+\sqrt{5})=8$

$\implies a(3-\sqrt{5})(3+\sqrt{5})=8$

$\implies4a=8$

$\implies a=2$

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

$\implies y=2(x-1-\sqrt{5})(x-1+\sqrt{5})$

Expand so that the equation is in standard form:

$\implies y=2(x^2-x+\sqrt{5}x-x+1-\sqrt{5}-\sqrt{5}x+\sqrt{5}-5)$

$\implies y=2(x^2-x-x+\sqrt{5}x-\sqrt{5}x+\sqrt{5}-\sqrt{5}+1-5)$

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

$\implies y=2x^2-4x-8$

6 0

2 years ago

Solve the equation using the Properties of Equality: 15a = – 2

Lostsunrise [7]

Answer:

a = - ------

Step-by-step explanation:

15 a = -2 (divide 15 on each side)

15a 2

----- = - ------

15 15

a = - ------

3 0

3 years ago

Question 8 - Find the mean

andre [41]

Answer:

You can hack it double click and press inspect for answers

Step-by-step explanation:

7 0

3 years ago

a 13 ft ladder is leaning against the house. The top of the ladder touches the house at ten ft above the ground. How far away is

Drupady [299]

Pythagoras theorem, answer is sqrt69 or 8.307 to 3dp.

7 0

3 years ago