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3 years ago

Which equation best represents the line?

Mathematics

1 answer:

erica [24]3 years ago

7 0

y = mx + b, where m = slope, and b = y-intercept.

y = 3x + 3

y = 1/2x - 3

y = 1/2x + 3

y = 3x + 1/2

we can eliminate 2 and 4 since the y-intercept in the graph is shown as (0, 3)

This leaves us with

y = 3x + 3 and y = 1/2x+3

m = change in y / change in x

We take any two points on the line to find the slope.

I chose (2, 4), (0, 3)

change in x: 2 - 0 = 2

change in y: 4 - 3 = 1

m = 1/2

This leaves us with the only answer that has the slope of 1/2 and the y-intercept of 3.

option: 3

y = 1/2x + 3

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3 years ago

Graph the linear equation and answer each of the following questions. y>2/3 x-2 What is the y-intercept? What is the slope (i

lozanna [386]

Answer:

(i)

y-intercept is -2

(ii)

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(iii)

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(iv)

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Step-by-step explanation:

We are given equation as

$y=\frac{2}{3} x-2$

now, we can compare it with slope intercept form of line

y=mx+b

where

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b is y-intercept

we get

$m=\frac{2}{3}$

$b=-2$

So,

(i)

y-intercept is -2

(ii)

slope is $\frac{2}{3}$

(iii)

we can see that

$m=\frac{2}{3}$

is a fraction and positive

so, slope is positive

(iv)

we can select any random value of x and find y

that will give us second point

Let's assume

x=3

$y=\frac{2}{3}\times 3-2$

$y=2-2$

$y=0$

So, another point is (3,0)

(v)

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3 years ago

Which equations represent the asymptotes of the hyperbola (x-1)^2/36-(y-2)^2/64=1 ?

allochka39001 [22]

Answer:

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Step-by-step explanation:

The asymptote equation of a translate hyperbola with equation $\frac{(x-h)^2}{b^2}-\frac{(y-k)^2}{a^2}=1$ is $y=\pm\frac{b}{a}(x-h)+k$

The given hyperbola has equation: $\frac{(x-1)^2}{36}-\frac{(y-2)^2}{64}=1$

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We have a=6 and b=8, h=1 and k=2.

We substitute this values to get:

$y=\pm\frac{6}{8}(x-1)+2$

$y=\pm\frac{4}{3}(x-1)+2$

$3y=\pm4(x-1)+6$

We split the plus or minus sign to get:

$3y=4x-4+6$

$3y=4x+2$

$3y-4x=2$

$3y=-4(x-1)+6$

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