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3 years ago

The equation of a line in slope intercept form that is perpendicular to y=-1/3 x +5 and goes through the point (-1,3)

Mathematics

1 answer:

sertanlavr [38]3 years ago

7 0

Answer:

y = 3x + 6

Step-by-step explanation:

The general equation of a line is;

y = mx + b

where m is the slope and b is the y intercept

The slope of the first line is -1/3

when two lines are perpendicular, the product of their slopes is equal to -1

Thus;

-1/3 * m2 = -1

-m2 = -3

m2 = 3

So the equation of the second line is;

y = 3x + b

To get b, we substitute the coordinates of the point (-1,3)

We substitute -1 for x and 3 for y

so, we have;

3 = 3(-1) + b

3 = -3 + b

b = 3 + 3

b = 6

So we have the second equation as;

y = 3x + 6

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Answer:

The coordinates of Jedds house are (-7 , -2)

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divide the distance between the two points

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ at the ratio

$(m_{1}:m_{1})$ , then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

∵ Hollis house is located at (-1 , 4)

∴ $(x_{1},y_{1})$ = (-1 , 4)

∵ She can walk in a straight line to get to Jedds house

∵ The restaurant is located at (-3 , 2) and partitions the way from

Hollis house to Jedds house by a ration of 1 : 2

∴ (x , y) = (-3 , 2)

∴ $(m_{1}:m_{1})$ = 1 : 2

- Lets consider that Jedds house is located at $(x_{2},y_{2})$

∴ $-3=\frac{-1(2)+x_{2}(1)}{1+2}$

∴ $-3=\frac{-2+x_{2}}{3}$

- Multiply both sides by 3

∴ $-9=-2+x_{2}$

- Add 2 for both sides

∴ $-7=x_{2}$

∴ $2=\frac{4(2)+y_{2}(1)}{1+2}$

∴ $2=\frac{8+y_{2}}{3}$

- Multiply both sides by 3

∴ $6=8+y_{2}$

- Subtract 8 for both sides

∴ $-2=y_{2}$

∴ The coordinates of Jedds house are (-7 , -2)

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Answer:

<1 and <6 = 98

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Step-by-step explanation:

82 + 9x - 6 + 6x - 1 = 180

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