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# Linear equations

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I keep getting the wrong answer on this one.

Find the distance between the x-intercept and the y-intercept of the graph of the equation 3x - 7y = 21 + 2x - 5y.

Apr 24, 2023

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Find the distance between the x-intercept and the y-intercept of the graph of the equation 3x - 7y = 21 + 2x - 5y

3x - 7y = 21 + 2x - 5y

Combine like terms.                         –7y + 5y  =  2x – 3x + 21

–2y  =  –x + 21

Multiply both sides by –1

this isn't necessary but it

makes it easy to work with.

Easier for me, anyway, LOL.                2y  =  x – 21

Set y = 0 and solve for x                                 x  =  21         That's your x-intercept.

Set x = 0 and solve for y                                 y  =  –10.5    That's your y-intercept.

Those are the values of the two legs of a right triangle, with the origin being the right angle.

If you draw it on a graph, it's obvious.

The line between the x- and y- intercepts is the hypotenuse of that right triangle.

Pythagoras' Theorem                         c2  =  (21)2 + (–10.5)2

c2  =  441 + 110.25  =  551.25

I used my calculator to

get this square root.                            c  =  23.48

.

Apr 24, 2023