Slope: Calculate the slope from two points

To solve this problem, let's follow these steps:

• Step 1: Identify the form of the given function
• Step 2: Compare the equation with the standard slope-intercept form
• Step 3: Extract the value of the slope from the equation

Now, let's work through each step:

Step 1: The given linear function is $y = -6x$. This is presented in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 2: Comparing $y = -6x$ with $y = mx + b$, we see that the equation lacks a constant term, indicating $b = 0$. The slope $m$ is the coefficient of $x$.

Step 3: The coefficient of $x$ is $-6$, so the slope $m$ is $-6$. Thus, the rate of change of the function is $-6$.

Therefore, the solution to the problem is $m = -6$.

To solve this problem, we'll follow these steps:

• Step 1: Recognize the given function $y = 10 - 2x$ and compare it to the standard linear form $y = mx + b$.
• Step 2: Identify the coefficient of $x$ which is $-2$.
• Step 3: Understand that this coefficient $-2$ is the slope or rate of change of the function.

Now, let's work through each step:
Step 1: The linear function provided is $y = 10 - 2x$.
Step 2: Comparing this with the standard linear form $y = mx + b$, we see that the coefficient of $x$ is $-2$.
Step 3: Therefore, the rate of change (or the slope) of the function is $m = -2$.

Thus, the rate of change of the linear function is $m = -2$.

To determine the rate of change of the function given by the equation $y = -2x + 1$, we will follow these steps:

• Step 1: Recognize that the equation is written in slope-intercept form, $y = mx + b$, where $m$ is the slope, or rate of change.
• Step 2: Identify the coefficient of $x$ in the given equation. Here, the equation $y = -2x + 1$ reveals that the coefficient of $x$ is $-2$.

This coefficient $-2$ directly represents the slope $m$ of the function.

Therefore, the rate of change of the function is $m = -2$.

To solve this problem, we need to find the rate of change, which is represented by the slope of the linear function.

The function provided is in the form $y = mx + b$, where $m$ is the slope. This is known as the slope-intercept form of a linear equation.

Given the equation $y = 14x + 13$, we can directly identify that the coefficient of $x$, which is 14, represents the slope $m$, or the rate of change of the function.

Therefore, the rate of change, or the slope, of this function is $m = 14$.

To identify the rate of change of the linear function $y = 7 - 3x$, we need to determine the slope of the equation.

The given function is in the form of $y = mx + b$, where $m$ is the slope or rate of change.

In the equation $y = 7 - 3x$, we notice that it can be rewritten as $y = -3x + 7$. Comparing this with the standard form $y = mx + b$, we find that the coefficient of $x$ is -3, meaning $m = -3$.

Therefore, the rate of change of this linear function is $-3$.

Thus, the correct answer is $m = -3$.

To solve this problem, we'll follow these steps:

• Identify the standard form of the linear function.
• Determine the coefficient of $x$, which is the slope $m$.

Now, let's work through each step:

Step 1: The given linear function is $y = 16 + 16x$, which is in the form $y = mx + b$.

Step 2: In this function, the coefficient of $x$ is $16$. This coefficient is the slope $m$ of the function.

Therefore, the rate of change of the function, or the slope, is $m = 16$.

To determine the rate of change of the linear function $y = 14 + 5x$, we need to identify the structure of the equation. We notice that it is given in the slope-intercept form $y = mx + b$, where $m$ is the slope or the rate of change.

In the equation $y = 14 + 5x$, the term involving $x$ is $5x$. Thus, the coefficient of $x$, which is $5$, represents the rate of change or slope of the function.

Therefore, the rate of change of the function is $m = 5$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the coordinates of the points.

• Step 2: Apply the slope formula.

• Step 3: Perform the arithmetic to calculate the slope.

Let's work through each step:

Step 1: Identify the given points:
Point $A$ is $(0, 7)$ and Point $B$ is $(8, -3)$.

Step 2: Use the slope formula, which is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of points $A$ and $B$:
Here, $(x_1, y_1) = (0, 7)$ and $(x_2, y_2) = (8, -3)$.

Step 3: Calculate the slope:
$m = \frac{-3 - 7}{8 - 0} \\ = \frac{-10}{8} \\ = -\frac{5}{4}$

Therefore, the slope of the graph is $-\frac{5}{4}$.

To find the slope of the graph of the linear function passing through points $A(2,10)$ and $B(-5,-4)$, we use the slope formula:

The slope formula is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute $(x_1, y_1) = (2, 10)$ and $(x_2, y_2) = (-5, -4)$:

$m = \frac{-4 - 10}{-5 - 2}$

Calculate the differences:

$y_2 - y_1 = -4 - 10 = -14$

$x_2 - x_1 = -5 - 2 = -7$

Substitute these into the slope formula:

$m = \frac{-14}{-7}$

Simplify:

$m = \frac{-14}{-7} = 2$

Therefore, the slope of the graph is $2$.

To determine the slope of the line passing through points $A(-3, 2)$ and $B(3, 2)$, we will use the slope formula:

The slope $m$ is calculated as:

Substituting the values from points $A(-3, 2)$ and $B(3, 2)$, we get:

The calculation shows that the difference in $y$-coordinates is zero, hence dividing by any non-zero number will result in a slope of zero. This indicates a horizontal line on the graph.

Therefore, the slope of the line is $0$.

To solve this problem, we need to calculate the slope of the line passing through the points $A(0, -10)$ and $B(4, 1)$.

The formula for the slope $m$ of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

Given the points $A(0, -10)$ and $B(4, 1)$, we identify:

• $x_1 = 0, y_1 = -10$
• $x_2 = 4, y_2 = 1$

Substituting these values into the slope formula, we have:

This simplifies to:

The fraction $\frac{11}{4}$ can be converted to a mixed number:

Therefore, the slope of the graph is $\bm{2\frac{3}{4}}$.

To find the slope ($m$) of the line passing through the points $A(0,7)$ and $B(-4,-9)$, we apply the slope formula:

First, assign the coordinates to the two points:

• $(x_1, y_1) = (0, 7)$
• $(x_2, y_2) = (-4, -9)$

Next, substitute these into the slope formula:

Simplify the expression:

The negative signs in the numerator and denominator cancel out:

Finally, divide to find the slope:

Therefore, the slope of the line passing through points $A(0,7)$ and $B(-4,-9)$ is $4$.