Question

the slope-intercept form of a linear equation is $y = mx + b$, where $x$ and $y$ are coordinates of an ordered pair, $m$ is the slope of the line, and $b$ is where the line crosses the $y$-axis. which is an equivalent equation solved for the slope, $m$? $m = \frac{y - b}{x}$; $m = y - \frac{b}{x}$; $m = \frac{y}{x} - b$; $m = yx + b$

Explanation:

Step1: Start with the slope - intercept form

We have the equation \(y = mx + b\). Our goal is to solve for \(m\). First, we need to isolate the term with \(m\). We can do this by subtracting \(b\) from both sides of the equation.
\(y - b=mx + b - b\)
Simplifying the right - hand side (since \(b - b = 0\)), we get \(y - b=mx\).

Step2: Solve for \(m\)

Now, to solve for \(m\), we divide both sides of the equation \(y - b = mx\) by \(x\) (assuming \(x
eq0\)).
\(\frac{y - b}{x}=\frac{mx}{x}\)
Since \(\frac{mx}{x}=m\) (for \(x
eq0\)), we have \(m=\frac{y - b}{x}\).

Answer:

\(m=\frac{y - b}{x}\) (the first option among the given options)