y = mx + b, where m = slope, b = the y - intercept.

is the line equation in slope intercept form

The line is parallel to -4x+7y=31 and since parallel lines have the same slope we need to find the slope of -4x+7y=31:

-4x+7y=31

y = (4/7)x + (31/7)

the slope is m = 4/7

y = (4/7)x + b

the line goes trough (8, 4) meaning for x = 8, y = 4. we plug these values in the equation y = (4/7)x + b to find b:

4 = (4/7)8 + b

by solving for b we find:

b = - 4/7

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the line equation in slope intercept form is:

y = (4/7)x - 4/7.