Consider the following linear equation. What is the slope, m, of the graph of this line?
Understand the Problem
The question is asking to identify the slope (m) of the given linear equation, which is in the form of y = mx + b. Here, we need to extract the coefficient of x from the equation to determine the slope.
Answer
The slope \( m \) is $-\frac{3}{4}$.
Answer for screen readers
The slope ( m ) is $-\frac{3}{4}$.
Steps to Solve
-
Identify the equation form The given equation is in the slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
-
Extract the slope In the equation ( y = -\frac{3}{4}x - 5 ), the coefficient of $x$ is $-\frac{3}{4}$. This value represents the slope $m$.
-
Write the value of the slope Thus, the slope ( m ) is:
$$ m = -\frac{3}{4} $$
The slope ( m ) is $-\frac{3}{4}$.
More Information
The slope indicates the rate of change of $y$ with respect to $x$. A negative slope means that as $x$ increases, $y$ decreases. The value $-\frac{3}{4}$ implies that for every 4 units you move to the right along the x-axis, you move down 3 units on the y-axis.
Tips
- Forgetting to identify the coefficient of $x$: Sometimes, students forget to identify the coefficient from the equation and confuse other constants with the slope. Always remember that the slope is the coefficient adjacent to $x$.
