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3 years ago

Write the equation of a line in slope intercept form given; (6,-3), (0, 5)

Mathematics

1 answer:

olganol [36]3 years ago

3 0

Answer:

$y=(-4/3)x+5$

Step-by-step explanation:

so you want to start by using y=mx+b

step one: find the slope (remember m is the slope in this)

m= $\frac{y2-y1}{x2-x1}$

m= $\frac{5+3}{0-6}$

m= $\frac{8}{-6}$

m= - $\frac{4}{3\\}$

step two: insert the value we found for m into the equation and take one of the given points and insert the x and y into the equation (im using (0,5)) and solve for b.

y=mx+b

5= -4/3(0)+b

5=b

step three: rewrite y=mx+b with the values we found for m and for b

$y=(-4/3)x+5$

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What are the coordinates of the image of the point (1-, 2) under a dilation of 3 with the origin

Gemiola [76]

Answer:

The image of the point (1, -2) under a dilation of 3 is (3, -6).

Step-by-step explanation:

Correct statement is:

<em>What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.</em>

From Linear Algebra we get that dilation of a point with respect to another point is represented by:

$\vec P' = \vec R + r\cdot (\vec P-\vec R)$ (Eq. 1)

Where:

$\vec R$ - Reference point with respect to origin, dimensionless.

$\vec P$ - Original point with respect to origin, dimensionless.

$r$ - Dilation factor, dimensionless.

If we know that $\vec R = (0,0)$ , $\vec P = (1, -2)$ and $r = 3$ , then the coordinates of the image of the original point is:

$\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]$

$\vec P' = (0,0) + 3\cdot (1,-2)$

$\vec P' = (3,-6)$

The image of the point (1, -2) under a dilation of 3 is (3, -6).

4 0

2 years ago

If f(x)=2x to the second power what is f(x) when x=3

Bad White [126]

<h3> ♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Just substitute 3 in:

2(3)^2 = 18

It would be 18

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0

3 years ago

Read 2 more answers

the game of monopoly is played on a square board with 10 spaces per side (so 40 in total). a player starts at the space marked "

lions [1.4K]

Answer:

Step-by-step explanation:

5 0

3 years ago

Which equation represents the circle described?

faust18 [17]

ANSWER

${(x - 4)}^{2} + {(y - 3)}^{2} = {2}^{2}$

EXPLANATION

The equation of the circle with radius r and centre (a,b) is given by

$(x - a)^{2} + {(x - b)}^{2} = {r}^{2}$

The radius is

$r = 2$

We need to determine the center of the circle from the given equation of another circle, which is,

${x}^{2} + {y}^{2} - 8x - 6y + 24 = 0$

We complete the square to obtain,

${x}^{2} - 8x+ {y}^{2} - 6y + 24 = 0$

${x}^{2} - 8x+ {y}^{2} - 6y = - 24$
${x}^{2} - 8x+ {( - 4)}^{2} + {y}^{2} - 6y + {( - 3)}^{2} = - 24 + {( - 3)}^{2} + {( - 4)}^{2}$

${(x - 4)}^{2} + {(y - 3)}^{2} = - 24 + 9+ 16$

${(x - 4)}^{2} + {(y - 3)}^{2} = 1$

The centre of this circle is (4,3)

Hence the center of the circle whose equation we want to find is also (4,3).

With this center and radius 2, the required equation is,

${(x - 4)}^{2} + {(y - 3)}^{2} = {2}^{2}$

Therefore the correct answer is C.

3 0

3 years ago

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Molodets [167]

I hope this helps you

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3 years ago