Mathematics, 16.07.2019 05:10 rmartinez044

What is the equation of the line that passes through the points (4/5,1/5) and (1/2,3/2)?

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Answer from: alaj6878

$y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})$ point-slope form

13x+3y=11 (standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using $\frac{y_2-y_1}{x_2-x_1}$ provided you are given two points on the line.

We are.

Now you can use that formula. But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

(4/5 , 1/5)

-( 1/2 , 3/2)

-----------------

3/10 -13/10

2nd/1st = $\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}$ is our slope.

So the following is point-slope form for a linear equaiton:

$y-y_1=m(x-x_1) \text{ where } m \text{ is slope and } (x_1,y_1) \text{ is a point on the line }$

Plug in a point $(x_1,y_1)=(\frac{1}{2},\frac{3}{2}) \text{ and } m=\frac{-13}{3}$ .

This gives:

$y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})$

I'm going to distribute:

$y-\frac{3}{2}=\frac{-13}{3}x-\frac{-13}{6}$

Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:

6y-9=-26x+13

Add 26x on both sides:

26x+6y-9=13

Add 9 on both sides:

26x+6y=22 This is actually standard form of a line.

It can be simplified though.

Divide both sides by 2:

13x+3y=11 (standard form)

Answer from: skykopystecky8769

$\large\boxed{y=-\dfrac{13}{3}x+\dfrac{11}{3}}-\bold{slope\ intercept\ form}\\\boxed{13x+3y=11}-\bold{standard\ form}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points

$\left(\dfrac{4}{5},\ \dfrac{1}{5}\right),\ \left(\dfrac{1}{2},\ \dfrac{3}{2}\right)$

Convert fractions to the decimals

(divide the numerator by the denominator) :

$\dfrac{4}{5}=0.8,\ \dfrac{1}{5}=0.2,\ \dfrac{1}{2}=0.5,\ \dfrac{3}{2}=1.5$

$\left(\dfrac{4}{5},\ \dfrac{1}{5}\right)=(0.8,\ 0.2)\\\\\left(\dfrac{1}{2},\ \dfrac{3}{2}\right)=(0.5,\ 1.5)$

Calculate the slope:

$m=\dfrac{1.5-0.2}{0.5-0.8}=\dfrac{1.3}{-0.3}=-\dfrac{13}{3}$

Put the value of slope and the coordinates of the first point to the equation of a line:

$0.2=-\dfrac{13}{3}(0.8)+b$ multiply both sides by 3

0.6=(-13)(0.8)+3b

0.6=-10.4+3b add 10.4 to both sides

11=3b divide both sides by 3

$\dfrac{11}{3}=b\to b=\dfrac{11}{3}$

Finally:

$y=-\dfrac{13}{3}x+\dfrac{11}{3}$ - slope-intercept form

Convert to the standard form (Ax + By = C):

$y=-\dfrac{13}{3}x+\dfrac{11}{3}$ multiply both sides by 3

3y=-13x+11 add 13x to both sides

13x+3y=11 - standard form

Answer from: Quest

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

Answer from: Quest

.24

step-by-step explanation:

the probability is .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

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