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2 years ago

14/15 - 3/5 simplified

Mathematics

1 answer:

Firlakuza [10]2 years ago

4 0

Answer:1/3

Step-by-step explanation:

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A line passes through the points (-1, -1)

Allisa [31]

Given:

A line passes through the points (-1, -1) and (5,8).

To find:

Which points lie on the same line?

Solution:

If a line passes through two points, then the equation of the line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:

$y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))$

$y+1=\dfrac{8+1}{5+1}(x+1)$

$y+1=\dfrac{9}{6}(x+1)$

$y+1=\dfrac{3}{2}(x+1)$

Multiply both sides by 2.

$2(y+1)=3(x+1)$

$2y+2=3x+3$

$2y=3x+3-2$

$y=\dfrac{3}{2}x+\dfrac{1}{2}$

So, the equation of the line is $y=\dfrac{3}{2}x+\dfrac{1}{2}$ .

Now, check each point for this equation.

Putting $x=-3$ , we get

$y=\dfrac{3}{2}(-3)+\dfrac{1}{2}$

$y=\dfrac{-9+1}{2}$

$y=\dfrac{-8}{2}$

$y=-4$

Similarly,

For $x=9,y=15$ .

For $x=1,y=2$ .

For $x=4,y=6.5$ .

For $x=3,y=5$ .

For $x=-2,y=-2.5$ .

Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.

6 0

3 years ago

Find the slope and the Y-intercept of the graph of y-6=3/8x

balandron [24]

Answer:

Slope =3/8

y-intercept is:(0,6)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Slope= -1/3 passing through (9,-2)<br>point slop form?<br>slope intercept form?

erica [24]

Point slope:
y-(-2)=-1/3(x-9)
slope intercept:
solve the point slope form
y+2 = -1/3x+3
y=-1/3x+1

6 0

2 years ago

If log(x + y) = log 3 + ½log x + ½log y, prove that x² + y² = 7xy

Free_Kalibri [48]

Answer:

See Explanation

Step-by-step explanation:

$log(x + y) = log3 + \frac{1}{2} logx+ \frac{1}{2} logy \\ \\ log(x + y) = log3 + logx ^{\frac{1}{2}} + logy ^{\frac{1}{2}}\\ \\ log(x + y) = log3 + log(xy) ^{\frac{1}{2}} \\ \\ log(x + y) = log[3(xy) ^{\frac{1}{2}}] \\ \\ x + y = 3(xy) ^{\frac{1}{2}} \\ \\ squaring \: both \: sides \\ {(x + y)}^{2} = \bigg(3(xy) ^{\frac{1}{2}} \bigg)^{2} \\ \\ {x}^{2} + {y}^{2} + 2xy = 9xy \\ \\ {x}^{2} + {y}^{2} = 9xy - 2xy \\ \\ \purple{ \bold{{x}^{2} + {y}^{2} = 7xy}} \\ thus \: proved$

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2 years ago

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The function f(x) is show on the graph. What is f(0)?

dexar [7]

Answer:

x = 0

Step-by-step explanation:

the origin

6 0

3 years ago