The basic structure of a linear function is y=mx+b (or +c, depending on your schools curriculum)

We need to find the slope (m), and the y-intercept (b/c)

To find the slope you can pick two random points, say (2,2) and (0,1)

The formula for the slope is this: m= y1-y2 / x1-x2

So if we substitute the points in, we get 2-1 / 2-0 = 1/2

Knowing the slope, it can be substituted into to the equation: y=1/2x + b

Then, if you notice the second point- (0,1), it’s the y-intercept. The y coordinate there is 1.

To check if this is correct, a random coordinate set can be picked and substituted in to find b.

y= 1/2x + b
2 = 1/2 *2 + b
2 = 1 + b
2-1=b
1=b

Therefore, the final linear function is y = 1/2 x + 1

3 0

3 years ago

Explain why 6:4 and 18:4 are not equivalent ratios?

bearhunter [10]

Answer:

False, 6:4 and 18:8 are equal ratios.

Step-by-step explanation:

Given data:

6:4 ≠ 18:8

Explanation.

1. 6:4 = 6/4 = 3/2

2. 18:8= 18/8 = 9/4 = 3/2

Hence proved:

6:4 = 18:8

8 0

2 years ago

Which of the following rational functions is graphed below?

vampirchik [111]

Answer:

The correct option is D.

i.e.

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$ is the correct option.

The correct graph is shown in attached figure.

Step-by-step explanation:

Considering the function

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$

$\mathrm{Domain\:of\:}\:\frac{1}{x\left(x+4\right)}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x$

$\mathrm{Range\:of\:}\frac{1}{x\left(x+4\right)}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:-\frac{1}{4}\quad \mathrm{or}\quad \:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{1}{4}]\cup \left(0,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{None}$

$\mathrm{Extreme\:Points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{Maximum}\left(-2,\:-\frac{1}{4}\right)$

So, the correct graph is shown in attached figure.

Therefore, the correct option is D.

i.e.

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$ is the correct option.

7 0

3 years ago

My mother is 43 years old.I am w years old. Write an expression as to how old we will both be in h year's time.​

My mother is 43 years old.I am w years old. Write an expression as to how old we will both be in h year's time.