The equation y=6x+1 is in "slope intercept" form. This form is y=mx+b and b is the y intercept and m is the slope.
This means we can read the slope and the intercept directly from the equation with no calculations.
The slope is 6 and the y intercept is 1 ( or the point (0,1) is you prefer)
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Solving the equation for "y" gives you the slope-intercept form.
y = -2x - 8
6x+3y = 18 3y = -6x+18 y = -2x+6 Therefore the slope is -2 and the y intercept is 6
6x+2y-3 = 0 2y = -6x+3 y = -3x+3/2 in slope intercept form
y=6x+12