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3 years ago

find the equation of a line through the coordinate (3,6) and parallel to the line represented by y=5/3 x-1

Mathematics

1 answer:

maw [93]3 years ago

5 0

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))

For lines to be parallel, their slopes have to be the SAME.

The given line's slope is 5/3, so the parallel line's slope is also 5/3

y = 5/3x + b

To find "b", plug in the point (3,6) into the equation

y = 5/3x + b

6 = 5/3(3) + b

6 = 5 + b

1 = b

y = 5/3x + 1

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3 Ximena draws an X shape in the coordinate plane as shown. Draw the images of

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<em>See attachment for the image of each rotation.</em>

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The top coordinates of the X shape are:

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$B = (1,0)$

$C = (3,0)$

$D =(4,0)$

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$(x,y) \to (-y,x)$

So, we have:

$A' = (0,0)$

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$C' = (0,3)$

$D' = (0,4)$

For 180 degrees rotation, the rule is:

$(x,y) \to (-x,-y)$

So, we have:

$A' = (0,0)$

$B' = (-1,0)$

$C' = (-3,0)$

$D' = (-4,0)$

For 270 degrees counter rotation, the rule is:

$(x,y) \to (y,-x)$

So, we have:

$A' = (0,0)$

$B' = (0,-1)$

$C' = (0,-3)$

$D' = (0,-4)$

See attachment for the image of each rotation