All categories

3 years ago

Write a linear function f with the values f(0) = 6 and f(4) = -6.

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

3 0

Answer:

f(x) = -3x + 6

Step-by-step explanation:

The general linear function is;

y = mx + b

it can also be written as (x , f(x))

f(x) = mx + b

where m is the slope and b is the y-intercept

so we have the points ;

(0,6) and (4,-6)

So we have;

for f(0) to be 6, it means that the y-intercept b is 6

This is because the value of x at the y-intercept is 0

So we have this as;

f(x) = mx + 6

Now, let’s substitute the other point so as to get m

For the other point;

x = 4 and f(x) = -6

that means;

-6 = 4m + 6

4m = -6-6

4m = -12

m = -12/4

m = -3

So we have the equation as;

f(x) = -3x + 6

You might be interested in

Y = 4(x - 2)(x + 6)<br> what is this factored out

lutik1710 [3]

Y=4x^2+16x-48

Start with factoring (x-2)(x+6) using distribution
Then multiply it by 4

4 0

3 years ago

Please can someone help me it’s urgent i need it done by 8:00‼️

OLEGan [10]

Answer: need to clam and not worry to much and study a lot to be come great and great at math

Step-by-step explanation: i try and i give it all i can and not give up

6 0

3 years ago

Could someone please help me on one of these and explian to me too? plz show work

Serhud [2]

Answer:

3) rate of change = -5/4

4) rate of change = 3

5) rate of change = 1

6) steepest slope = #4

7) Please see the attached graph and explanation below

8) Please see the attached graph and explanation below

Step-by-step explanation:

I will do questions 3, 4, 6, 7, and 8, and will let you work on question 5 (since it involves the same process of solving for the rate of change as questions 3 and 4). However, the rate of change for question 5 is 1.

<h3>3) Calculate the Rate of Change from the Graph: </h3>

The <u>rate of change</u> is essentially the same as the <em>slope</em> of a linear equation, where it represents the ratio of a change in y to a corresponding change in x.

In order to solve for the rate of change, choose two points from the given graph.

Let (x₁, y₁) = (0, 200)

(x₂, y₂) = (80, 100)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (100 - 200)/(80 - 0)

m = -100/80

Reduce to lowest terms by dividing the numerator and the denominator by 20/20:

m = -5/4

Therefore, the rate of change is -5/4.

<h3>4) Calculate the Rate of Change from the Table: </h3>

Similar to what we did in question 3, choose two ordered pairs from the given table:

Let (x₁, y₁) = (0, -1)

(x₂, y₂) = (3, 8)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

$m = \frac{8 - (-1)}{3 - 0}$

$m = \frac{8 + 1 }{3}$

$m = \frac{9}{3}$

m = 3

Therefore, the rate of change from the given table is 3.

<h3>6) Which linear function has the steepest slope? </h3>

The positive-sloped lines whose rate of change has the highest value will have the steepest slope. For lines with negative slopes (downward-tilting lines), the highest absolute value for its rate of change will have the steepest negative slope.

Hence, the linear function with the steepest slope is #4 because the value of y changes by 3 units for every unit of change in x values.

<h3>7) Graph the equation: y = -6x - 4:</h3>

The linear equation, y = -6x - 4, where the slope, m = -6, and the y-intercept is (0, -4).

To graph this equation, start by plotting the y-intercept.
Then, use the slope, m = -6/1 (down 6 units, run 1 unit to the right) to plot other points on the graph. In doing so, your next graph should occur at point, (1, -10). Connect the two points to create a line that will represent the given equation, y = -6x - 4.

Technically, two points are sufficient enough to connect and create a line with. Please see the attached screenshot of the graph for y = -6x - 4.

<h3>8) Graph the following equation: 3x - 4y = 12</h3>

The given linear equation is in its <u>standard form</u>, Ax + By = C. It is easier to graph when the equation is in its <u>slope-intercept form,</u> y = mx + b.

In order to transform the given standard equation to slope-intercept form, start by subtracting 3x from both sides:

3x - 4y = 12

3x -3x - 4y = -3x + 12

-4y = -3x + 12

Divide both sides by -4 to isolate y:

$\frac{-4y}{-4} = \frac{-3x + 12}{-4}$

y = ¾x - 3 ⇒ This is the slope-intercept form where the slope, m = ¾, and the y-intercept is (0, -3).

<h3><u>Graph:</u></h3>

Similar to how we graphed the equation from question 7, start by plotting the y-intercept (0, -3) on the graph. Then, use the slope, m = ¾ (3 units up, 4 units run), to plot other points on the graph. Your next point occurs at the <u>x-intercept</u>, (4, 0). The <em>x-intercept</em> is the point on the graph where it crosses the x-axis. Connect the two points to create a line that will represent the given equation, 3x - 4y = 12.

Please see the attached screenshot of the graph for 3x - 4y = 12.