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1 year ago

9. Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5,-3)

Mathematics

1 answer:

Crazy boy [7]1 year ago

3 0

Answer:

$y = - \frac{2}{ 3} x + \frac{1}{3}$

Step-by-step explanation:

either pick the generic line in slope-intercept form

$y = mx + q$

and plug y and x from the points in there, you get two conditions on m and q and find the values or...

Between the two points you get that when x increases (from 2 to 5) by 3 units, y decreases (from -1 to -3) by 2 units. You can rule out the first two options since the slope cannot be an integer. from the other 2, try x=5 into both to see which one gives -3 for y.

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Which graph shows y < x² +1?<br> O<br> 4) Intro<br> •

Ket [755]

The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.

<h3>How to graph an inequality?</h3>

The steps to graph an inequality equation are:

Solve for the variable y in the given equation
Graph the boundary line for the inequality
Shade the region that satisfies the inequality.

<h3>Calculation:</h3>

The given inequality is y < x² + 1

Finding points to graph the boundary line by taking y = x² + 1:

When x = -2,

y = (-2)² + 1 = 4 + 1 = 5

⇒ (-2, 5)

When x = -1,

y = (-1)² + 1 = 2

⇒ (-1, 2)

When x = 0,

y = (0)² + 1 = 1

⇒ (0, 1)

When x = 1,

y = (1)² + 1 = 2

⇒ (1, 2)

When x = 2,

y = (2)² + 1 = 5

⇒ (2, 5)

Plotting these points in the graph forms an upward-facing parabola.

So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.

From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".

Learn more about graphing inequalities here:

brainly.com/question/371134

#SPJ1

5 0

1 year ago

Read 2 more answers

The perimeter of a rectangle is 68 inches. Its width is 16 inches. What is its length? A 16 inches B 18 inches C 20 inches D 22

Phantasy [73]

Answer: 18

Step-by-step explanation:

8 0

2 years ago

Find the first term and common difference of an AP, whose 7th term is 29/6 and 15th term is 11/2.

777dan777 [17]

Answer:

The first term is 13/3 and the common difference is d = 1/12

The formula is a(n) = 13/3 + (1/12)(n - 1)

Step-by-step explanation:

The general equation for an arithmetic progression is:

a(n) = a(1) + d(n - 1), where d is the common difference/

Case 1: n = 7: 29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)

Case 2: n = 15: 11/2 = a(1) + d(15 - 1) = a(1) + d(14)

Then our system of linear equations is:

a(1) + 6d = 29/6

a(1) + 14d = 11/2

Let's solve this by elimination by addition and subtraction. Subtract the first equation from the second. We get:

Substituting 1/12 for d in the first equation, we get:

a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)

Then a(1) = 66/12 - 14/12 = 52/12 = 13/3

The first term is 13/3 and the common difference is d = 1/12

The arithmetic sequence formula for this problem is thus:

a(n) = 13/3 + (1/12)(n - 1) 8

5 0

2 years ago

How do i convert 2.3 y/min to ft/s

Mama L [17]

2.3 meters per second = 7.546 feet per second

Formula: multiply the value in meters per second by the conversion factor '3.2808398950087'.

So, 2.3 meters per second = 2.3 × 3.2808398950087 = 7.54593175852 feet per second.

5 0

2 years ago

Read 2 more answers

Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card how many spaces forward or

Ivenika [448]

Complete question :

designs a board game in which a card is drawn on each turn. • A blue card means move forward 4 squares. • A red card means move back 6 squares. Liam suggests adding some other cards to Sia's game Part A Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card. How many spaces forward or backward does a player move after drawing a yellow card? Justify your answer.

Answer:

2 squares backward

Step-by-step explanation:

Given the rule :

Blue card = 4 squares forward

Red card = 6 squares backward

Yellow card = drawing a blue followed by a red

Spaces moved after drawing a yellow card:

Yellow equals :

Blue = + 4 squares ; then

Red = - 6 squares

Net total movement :

Blue + red

+4 + (-6)

4 - 6

- 2

2 squares backward

7 0

2 years ago