The slope-intercept form of a linear equation is $y=m x+b$, 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, $m$?
A. $m=y x+b$
B. $m=\frac{y-b}{x}$
C. $m=\frac{y}{x}-b$
D. $m=y-\frac{b}{x}
Answer (1)
Start with the slope-intercept form: y = m x + b .
Subtract b from both sides: y − b = m x .
Divide both sides by x : x y − b = m .
The equation solved for m is: m = x y − b .
Explanation
Understanding the Equation We are given the slope-intercept form of a linear equation: y = m x + b , where m represents the slope, and we want to solve for m .
Subtracting b To isolate m , we first subtract b from both sides of the equation: y − b = m x + b − b y − b = m x
Dividing by x Next, we divide both sides by x to solve for m :
x y − b = x m x x y − b = m
Final Equation for m Therefore, the equation solved for the slope m is: m = x y − b
Examples
In real life, understanding the slope-intercept form and solving for the slope can help you analyze various linear relationships. For example, if you are tracking the cost of a taxi ride, y represents the total cost, x represents the distance traveled, m is the cost per mile (slope), and b is the initial fee. If you know the total cost and the initial fee, you can calculate the cost per mile (slope) using the formula we derived.
