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3 years ago

What type of equation would best model this data

Mathematics

1 answer:

Contact [7]3 years ago

7 0

A linear equation would likely work nice here due to that it's going up the whole time in somewhat of a straight line if you plot the points

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This table gives a few (x, y) pairs of a line in the coordinate plane. What is the x-intercept of the line?

PIT_PIT [208]

Answer:

x=-14

Step-by-step explanation:

The x-intercept of a line is the value of x that makes y=0.

A line can be expressed in its slope-intercept form:

y=mx+b

Once determined the equation of the line, the x-intercept can be calculated by setting y=0 and solving for x.

Let's find the slope of the line.

Suppose we know the line passes through two points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Let's pick the first two points of the table (-94,24) (-74,18). The slope is:

$\displaystyle m=\frac{18-24}{-74+94}=\frac{-6}{20}=-\frac{3}{10}$

The equation of the line is:

$\displaystyle y=-\frac{3}{10}x+b$

Now use one of the points to find b, for example (-94,24):

$\displaystyle 24=-\frac{3}{10}\cdot (-94)+b$

Operating:

$\displaystyle 24=\frac{141}{5}+b$

Solving:

$b=24-\frac{141}{5}=-\frac{21}{5}$

The complete equation of the line is:

$\displaystyle y=-\frac{3}{10}x-\frac{21}{5}$

To find the x-incercept, set y=0 and solve:

$\displaystyle 0=-\frac{3}{10}x-\frac{21}{5}$

$\displaystyle x=\frac{\frac{21}{5}}{-\frac{3}{10}}=-\frac{21}{5}\cdot \frac{10}{3}$

x=-14

5 0

3 years ago

Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220

Doss [256]

Answer:

1,000 km

Step-by-step explanation:

Assume that when two train pass each other, Lian has traveled x (km)

=> The time Lian has traveled when two trains pass each other is:

Time = Distance/ Rate = x/ 250 (hour)

As Lian and Yuto travelled from the two opposite train stations and the train stations are 1,880 km apart

=> When two train pass each other, Yuto has traveled 1,880 - x (km)

=> The time Yuto has traveled when two trains pass each other is:

Time = Distance/ Rate = (1,880 - x)/220 (hour)

As Lian and Yuto board at the same time, so that when two trains pass each other, the time both of them have traveled is equal

=> x/ 250 = (1,880 - x)/220

=> 220x = 250 x (1,880 -x)

=> 220x = 470,000 - 250x

=> 470x = 470,000

=> x = 1,000

So that, when two train pass each other, Lian has traveled x = 1,000 km

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marusya05 [52]

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3 years ago

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What is the equation of a line parallel to the line y = 4x + 7 and passes through the point (3, 0)?

KATRIN_1 [288]

Two lines to be parallel their slopes have to be equal.

so m1 = m = 4

y = mx + b ( Slope intercept form)

y = 4x + b

(3,0) is on the line:

0 = 12 + b

b = -12

y = 4x - 12

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3 years ago

1 +32-10 divided by 2

Step2247 [10]

answer.11.5

by the rule of bodmas first add and sunstract and divided

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