Question

Solve s = r0 for 0
Rearrange the formula y = mx + b for m

Answer 1

To solve the equation y = mx + b for m, subtract b from both sides of the equation and then divide both sides by x.

Step-by-step explanation:

To solve the equation y = mx + b for m, we need to isolate the variable m on one side of the equation. We can do this by subtracting b from both sides of the equation:

y - b = mx

Now, we can divide both sides of the equation by x to solve for m:

m = (y - b) / x

So the formula for m in the equation y = mx + b is m = (y - b) / x.

Answer 2

For s = r0, rearranging for r gives: r = s / 0.

For y = mx + b, rearranging for m gives: m = (y - b) / x.

Step-by-step explanation:

To rearrange the formula s = r0 for r, divide both sides of the equation by 0: r = s / 0. This expression becomes undefined since division by 0 is not possible in mathematics. Therefore, the equation s = r0 does not have a valid solution for r when rearranged.

For the equation y = mx + b representing a linear equation in slope-intercept form, to isolate the slope (m), rearrange the formula. Begin by subtracting b from both sides to get: y - b = mx. Then, divide both sides by x to solve for m: m = (y - b) / x. This rearrangement isolates the slope (m), showing that the slope of a line (m) is the change in y divided by the change in x, represented as the rise over the run in a Cartesian coordinate system.

This rearrangement helps in understanding how changes in x and y affect the slope of a linear equation and how the slope-intercept form of a line can be used to graph lines or analyze linear relationships between variables.