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3 years ago

What is the equation in standard form for (0,3) and (7,0)

Mathematics

1 answer:

Luden [163]3 years ago

3 0

Answer:

3x + 7y = 21

Step-by-step explanation:

We have value of two points (0,3) and (7,0)

First, let's find the slope of this line. The formula for slope is:

Change in y/Change in x or (y₂ - y₁)/(x₂-x₁)

Where x₁ = 0 x₂= 7 y₁ = 3 y₂ = 0

(y₂ - y₁)/(x₂-x₁)

= (0-3)/(7-0)

=-3/7

Now we can write the equation in point-slope form:

y-y₁ = m(x-x₁)

y - 3 = -3/7(x-0)

y-3=-3x/7

y=-3x/7 + 3

Now let's convert this to standard form, by making the y-intercept by itself:

Ax + By = C

y=-3x/7 + 3

Multiply through by 7

7(y) = 7(-3x/7) + 7(3)

7y = -3x + 21

3x + 7y = 21

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1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)

Sveta_85 [38]

Answer:

1. $-5x+3y+44=0$

2. $2x+y-2=0$

3. $2x+y-4=0$

Step-by-step explanation:

Standard form of a line is $Ax+By+C=0$ .

If a line passing through two points then the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope, i.e., $m=\dfrac{y_2-y_1}{x_2-x_1}$ .

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

$y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)$

$y+3=\dfrac{-5}{-3}(x-7)$

$y+3=\dfrac{5}{3}(x-7)$

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$3y+9=5x-35$

$-5x+3y+9+35=0$

$-5x+3y+44=0$

Therefore, the required equation is $-5x+3y+44=0$ .

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to $2 x + y =-5$ .

Slope of the line : $m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2$

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

$y-2=-2(x-0)$

$y-2=-2x$

$2x+y-2=0$

Therefore, the required equation is $2x+y-2=0$ .

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to $2x + y =-5$ .

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

$y-0=-2(x-2)$

$y=-2x+4$

$2x+y-4=0$

Therefore, the required equation is $2x+y-4=0$ .

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Step-by-step explanation: The Earth is one astronomical unit from the sun i.e.1AU= 93 million miles.The angular speed of the Earth traveling around the sun is approximately 0.9863 degrees per day. If we assume the orbit of the Earth is completely circular, what is the linear speed in miles per hour?

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x = (2*pi*0.0411)/(360)

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X is how much the Earth travels per hour in Radians.

Multiplying per Radius:

Earth distance traveled per hour = 0.0667117 * $10^{6}$ miles

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