name as many pairs of points so that the line is passing through them slopes given below

Question

the slopes below are what we need to find the pairs passing through the line

5/3

 -2/7

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4

-8

0

Answer 1

y-k=5(x-h)/3 represents all lines with a slope of 5/3. When x=h, y=k.

So, if h and k are both zero, y=5x/3 passing through the origin. If h=1 and k=1, y-1=5(x-1)/3, y=5x/3-5/3+1=5x/3-2/3 or (5x-2)/3. The y-intercept is -2/3 and the x-intercept is 2/5. So the general equation for all lines with the slope 5/3 is:

3y-3k=5x-5h, that is, 5x-3y+3k-5h=0.

For slope -2/7, we have y-k=-2(x-h)/7, 7y-7k=-2x+2h, 2x+7y-7k-2h=0.

For undefined slope (infinite): vertical line: x=h.

Slope 4: y=4(x-h)+k, y=4x-4h+k or 4x-y+k-4h=0.

Slope -8: y=-8(x-h)+k, y=-8x+8h+k, 8x+y-k-8h=0.

Slope 0: horizontal line: y=k.

Note that h and k can be any numbers in all cases, so (h,k) represents the points that the lines pass through.