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umka2103 [35]
3 years ago
14

a linear function passes through the point (1,5)and (7,23)what are the rate of change and initial value?

Mathematics
1 answer:
Vlada [557]3 years ago
4 0

Answer:

The rate of change = 3

Initial value = 2

Step-by-step explanation:

The linear function has the form ⇒ y = mx + c

Where m is the slope or the rate of change, and c is y-intercept.

Given: A linear function passes through the point (1,5)and (7,23)

So, m = (y₂-y₁)/(x₂-x₁) = (23-5)/(7-1) = 18/6 = 3

So, y = 3x + c

By substitution with the point (1,5)

So, at x = 1 , y = 5

5 = 3*1 + c

c = 5 - 3 = 2

∴ y = 3x + 2

so, the rate of change = 3

And initial value = 2

initial value is the value at which x = 0 which is the y-intercept

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Write the equation of the line that passes through the points (0,8) and (-1, –4).
andrey2020 [161]

Answer:

Step-by-step explanation

First, let's remember the equation for point-slope form and how to find the 'm' value:

y-y1 = m (x-x1)\\m = rise/run\\m = \frac{-4-(8)}{-1-(0)} = 12

Now plug your m value and (x1, y1) into point-slope form:

y - 8 = 12(x-0)\\reduce\\y=12x+8

8 0
3 years ago
The perimeter of a rectangle is 22 inches. Find the dimensions if its length is 3 inches greater than its width.
MaRussiya [10]

Answer:

Length: 7

Width: 4

Step-by-step explanation:

We can create a system of equations for this problem, where w is the width and l is the length.

The perimeter of a rectangle is twice its length added to twice its width.

2l+2w=22

The length is 3 more than the width:

l = w+3

We can now substitute in w+3 as l in the equation 2l+2w=22.

2(w+3) + 2w = 22

Distribute the first terms:

2w+6+2w=22

Combine like terms:

4w+6=22

Subtract 6 from both sides:

4w=16

Divide both sides by 4:

w = 4

Now we know that w = 4. We can now substitute this inside an equation to find l.

l = w+3\\\\l = 4+3\\\\l=7

Hope this helped!

7 0
3 years ago
Solving linear equations
AlexFokin [52]

Answer:

(x, y ) = ( \frac{1}{2}, \frac{5}{2})

Step-by-step explanation:

given the 2 equations

4x + 2y = 7 → (1)

y = 5x → (2)

Substitute y = 5x into equation (1)

4x + 2(5x) = 7

4x + 10x = 7

14x = 7 ( divide both sides by 14 )

x = \frac{7}{14} = \frac{1}{2}

substitute this value into equation (2)

y = 5 × \frac{1}{2} = \frac{5}{2}


4 0
3 years ago
A parallelogram with a height of 2x+3 has an area of 2x^2+13x+15. What is the length of the base of the parallelogram? Please sh
OlgaM077 [116]

(2x^2+13x+15)/2x+3=x+5

Use long or synthetic division to solve this problem.

8 0
3 years ago
Read 2 more answers
What is the value of x in the model below? <br> Enter your answer in the box.
sp2606 [1]

It looks like the scale is balanced so that means you can set one side equal to the other which leaves you with the equation x+(-10)=-16

To get x by itself add x to each side to get x=-6

X=-6 is your answer

3 0
3 years ago
Read 2 more answers
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