help, math help!?

Question

please solve and explain b/c i do not understand these:

Write an equation of the line which has the given slope, m, and which passes through the given point. m= -5; ( 9,1)




Write an equation of the line which has the given slope, m, and which passes through the given point: m = - 1/2 ; (8, -5)

For the first one i got

1y= -5(9) +b


and for the second i got

-5y= -1/2(8)+b



are these right

Answer 1

No, your solutions are not correct.
The general form of the line equation is:
y = kx + b, where k is the slope (in this case m) so:
(1) y = -5x +b
(2) y = -0.5x +b
we can use the given point to determine the value b. Since the point must satisfy the equation, we have:
(1) 1 = -5*9 + b, so b = 46 and hence y = -5x + 46
(2) -5 = -0.5*8 + b, so b = -1 and hence y = -0.5x - 1

There are other forms of line equation which may lead to the same result. For example, consider an arbitrary point on the line: (x, y). Combine with the given point(x_0, y_0), we have the definition of the slope as:
m = (y - y_0)/(x - x_0)
thus:
(1) -5 = (y-1)/(x-9), or y = -5x + 46
(2) -0.5 = (y + 5)/(x - 8), or y = -0.5x - 1