Explain slopes and linear relationships. what does the formula y=mx+b mean and how do you plug in numbers to solve it? ?

Y=mx+b describes a linear relationship; m is the slope, b is the y-intercept.

slope is the change in height over the change in horizontal distance; sometimes these are referred to as the "rise" and "run," making slope equal to rise over run. a bigger slope means a bigger rise, which means a steeper slope.

the y-intercept is where the line intercepts(crosses) the y-axis. the best way to think about this: if a point is on the y-axis, its x-coordinate has to be 0. if the x-coordinate was a positive number, the point would be to the right of the y-axis, and if it were a negative number, it would be to the left of the y-axis.

keeping this in mind, we can find out the y-intercept of an equation y = mx + b by plugging 0 in for x, since we know the x-coordinate has to be zero:

y = mx + b
y = m(0) + b
y = b

that is why b is the y-intercept.

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for the problem you gave in the comments:
mack charges $8 per hour, plus a flat fee of $2.50. we can write a formula for how much mack gets paid, based on h = number of hours he babysits:
p = 8h + 2.5
p is how much he is paid, and h is the number of hours he babysits. if he babysits for 1 hour:
p = 8(1) + 2.5
p = 10.5
he gets paid $10.50.