Find an equation of the line with the given slope that passes through the given point. Write the equation in the form Ax+By=C.
m=6/5, (3, -7)
The equation of a line in point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We are given the slope m = 6/5 and the point (3, -7), so we have:
y - (-7) = (6/5)(x - 3)
y + 7 = (6/5)x - (6/5)(3)
y + 7 = (6/5)x - 18/5
Now, we can rewrite the equation in the form Ax + By = C by moving all terms to the left side of the equation:
(6/5)x - y = -7 - 18/5
(6/5)x - y = -7 - (18/5)
(6/5)x - y = (-7)(5/5) - (18/5)
(6/5)x - y = -35/5 - 18/5
(6/5)x - y = -53/5
Therefore, the equation of the line with slope m = 6/5 that passes through the point (3, -7) is:
(6/5)x - y = -53/5.