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4 years ago

Write the slope-intercept form of the equation that passes through the given points. (separate equations for each of them)

Mathematics

1 answer:

guajiro [1.7K]4 years ago

6 0

Answer:

Part 1) $y=-\frac{1}{5}x-1$

Part 2) $y=3x-16$

Part 3) $y=4$

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

Part 1) we have

(10,-3) (5,-2)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{-2+3}{5-10}$

$m=\frac{1}{-5}$

$m=-\frac{1}{5}$

Find the value of b

we have

$m=-\frac{1}{5}$

$point (10,-3)$

substitute in the equation $y=mx+b$ and solve for b

$-3=-\frac{1}{5}(10)+b$

$-3=-2+b$

$b=-3+2=-1$

substitute

$y=-\frac{1}{5}x-1$

Part 2) we have

(6,2) (7,5)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{5-2}{7-6}$

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

$m=3$

Find the value of b

we have

$m=3$

$point (6,2)$

substitute in the equation $y=mx+b$ and solve for b

$2=3(6)+b$

$2=18+b$

$b=2-18=-16$

substitute

$y=3x-16$

Part 3) we have

(4,4) (-7,4)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{4-4}{-7-4}$

$m=\frac{0}{-11}$

$m=0$

This is a horizontal line (parallel to the x-axis)

The y-intercept b is equal to the y-coordinate

therefore

The equation of the line is

$y=4$

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Do the lines -x+5y=22 and 7x-2y=19 intersect

melomori [17]

Yes, they intersect at roughly (4.2,5.2).

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4 years ago

Which equation represents the magnitude of an

Basile [38]

Answer:

$M=\log{(100S)}$

Step-by-step explanation:

The Richter scale, the standard measure of earthquake intensity, is a logarithmic scale, specifically logarithmic base 10. This means that every time you go up 1 on the Richter scale, you get an earthquake that's 10 times as powerful (a 2.0 is 10x stronger than a 1.0, a 3.0 is 10x stronger than a 2.0, etc.).

How do we compare two earthquake's intensities then? As a measure of raw intensity, let's call a "standard earthquake" S. What's the magnitude of this earthquake? The magnitude is whatever power of 10 S corresponds to; to write this relationship as an equation, we can say $10^m=S$ , which we can rewrite in logarithmic form as $m=\log{S}$ .

We're looking for the magnitude M of an earthquake 100 times larger than S, so reflect this, we can simply replace S with 100S, giving us the equation

$M=\log{(100S)}$ .

To check to see if this equation is right, let's say we have an earthquake measuring a 3.0 on the Richter scale, so $3=\log{S}$ . Since taking 100 times some intensity is the same as taking 10 times that intensity twice, we'd expect that more intense earthquake to be a 5.0. We can expand the equation $M=\log{(100S)}$ using the product rule for logarithms to get the equation

$M=\log{(100S)}=\log{100}+\log{S}$

And using the fact that $\log{100}=2$ and our assumption that $\log{S}=3$ , we see that $M=2+3=5$ as we wanted.

3 0

4 years ago

(08.07 HC)

katovenus [111]

Answer:

Below in bold.

Step-by-step explanation:

Part A

At the x-intercepts f(x) = 0, therefore:

2x^2 - 3x - 5 = 0

(2x - 5)(x + 1) = 0

x = 5/2, -1)

So the x intercepts are (-1, 0) and (5/2, 0).

Part B

The Coefficient of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.

Convert f(x) to vertex form, by completing the square:

f(x) = 2x^2 - 3x - 5

= 2(x^2 - 3/2x) - 5

= 2[(x - 3/4)^2 - 9/16] - 5

= 2(x - 3/4)^2 -18/16 - 80/16

= 2(x - 3/4)^2 - 49/8

So the coordinates of the vertex are

(3/4, -49/8) or

(0.75, -6.125) in decimal form.

Part C

To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.

The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).

You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.

Suggest x = - 2 and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 = 11.

- that is the point (-2,11) and the other would be x = 4, f(x) = 15. (4, 15)

Once you have plotted these points draw a smooth u shaped curve through them.

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2 years ago

Why is a right equilateral triangle impossible?

Tom [10]

Because in an equilateral triangle all angles should measure 60 degrees otherwise all sides would not be equal.

5 0

3 years ago

775 tickets were sold for a game for a total of 1,187.50. If adults tickets sold for 2.50 and children's tickets sold for 1.00 h

Ivanshal [37]

Answer: 275 adult tickets and 500 children's tickets were sold.

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of children's tickets that were sold.

775 tickets were sold for the game. It means that

x + y = 775

If adults tickets sold for 2.50 and children's tickets sold for 1.00 and all the tickets were sold for a total of 1,187.50, it means that

2.5x + y = 1187.5

Substituting x = 775 - y into equation 1, it becomes

2.5(775 - y) + y = 1187.5

1937.5 - 2.5y + y = 1187.5

- 2.5y + y = 1187.5 - 1937.5

- 1.5y = - 750

y = - 750/ - 1.5

y = 500

x = 775 - y = 775 - 500

x = 275

6 0

3 years ago