Question

Which equatios are already in y=mx+b form

Answer 1

The equation \(y = mx + b\) describes a linear equation where:
- \(y\) is the dependent variable,
- \(m\) is the slope of the line,
- \(x\) is the independent variable,
- \(b\) is the y-intercept (the value of \(y\) when \(x = 0\)).

To determine if an equation is already in the form \(y = mx + b\), you should verify that \(y\) is isolated on one side of the equation and that the equation is linear in terms of \(x\).

Here are some examples of equations in the \(y = mx + b\) form:

1. \(y = 2x + 3\)
2. \(y = -0.5x + 4\)
3. \(y = 7x - 1\)

Here are examples of equations not in \(y = mx + b\) form, which you would need to rearrange:

1. \(2x + 3y = 6\) (needs rearranging to become \(y = -\frac{2}{3}x + 2\))
2. \(x - y = 5\) (needs rearranging to become \(y = x - 5\))
3. \(y^2 = 4x + 1\) (not linear, so cannot be rearranged into \(y = mx + b\))

If you provide specific equations, I can help you determine whether they are in \(y = mx + b\) form.