Linear Function y=mx+b: Calculate the slope from two points

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

• Step 1: Identify the coordinates of the given points.
• Step 2: Apply the slope formula.
• Step 3: Perform the subtraction and division required by the formula.

Now, let's work through each step:
Step 1: We have the points $(x_1, y_1) = (6, 19)$ and $(x_2, y_2) = (12, 20)$.
Step 2: The formula for the slope $m$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Step 3: Substituting the values, we get $m = \frac{20 - 19}{12 - 6} = \frac{1}{6}$.

Therefore, the slope of the line that passes through the points is $m = \frac{1}{6}$.

To find the slope of the line passing through the points $(0, 0)$ and $(5, -5)$, we will use the slope formula. Let's follow these steps:

• Step 1: Identify the points as $(x_1, y_1) = (0, 0)$ and $(x_2, y_2) = (5, -5)$.
• Step 2: Substitute these values into the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Step 3: Perform the calculation:
  $m = \frac{-5 - 0}{5 - 0} = \frac{-5}{5} = -1$

The calculation shows that the slope $m$ is $-1$.

Therefore, the solution to the problem is $m = -1$.

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

• Step 1: Identify and assign coordinates
• Step 2: Apply the slope formula
• Step 3: Simplify the calculations

Let's proceed with each step:

Step 1: Assign coordinates from the given points:
$(x_1, y_1) = (3, 6)$ and $(x_2, y_2) = (10, 20)$.

Step 2: Apply the slope formula, which is:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 6}{10 - 3}$.

Step 3: Calculate the slope:

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

Therefore, the slope of the line passing through the points $(3, 6)$ and $(10, 20)$ is $m = 2$.

The correct choice from the given options is $m = 2$.

To find the slope of the line that passes through the points $(-2, -4)$ and $(2, 4)$, we use the slope formula:

• The slope $m$ is calculated using $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Plugging in the given points, $(x_1, y_1) = (-2, -4)$ and $(x_2, y_2) = (2, 4)$, we have:

$m = \frac{4 - (-4)}{2 - (-2)}$

$m = \frac{4 + 4}{2 + 2}$

$m = \frac{8}{4}$

After simplifying, we find:

$m = 2$

Therefore, the slope of the line is $m = 2$, corresponding to choice 3.

To solve this problem, we'll calculate the slope of the line passing through the points $(2, 2)$ and $(9, 16)$.

• Step 1: Identify the coordinates
• Step 2: Apply the slope formula
• Step 3: Simplify the expression

Let's proceed:

Step 1: The coordinates given are $(x_1, y_1) = (2, 2)$ and $(x_2, y_2) = (9, 16)$.

Step 2: The slope $m$ of a line through two points is given by:

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

Substituting the coordinates into the formula, we have:

$m = \frac{16 - 2}{9 - 2}$

Step 3: Simplify the expression:

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

$m = 2$

Therefore, the slope of the line is $\mathbf{m = 2}$.

To solve this problem, we'll calculate the slope of the line passing through the points $(3, 7)$ and $(6, 14)$. The formula for the slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

• $m = \frac{y_2 - y_1}{x_2 - x_1}$

First, we identify our points as follows:
Point 1: $(x_1, y_1) = (3, 7)$
Point 2: $(x_2, y_2) = (6, 14)$

Next, apply the formula:
$x_1 = 3 \\ y_1 = 7 \\ x_2 = 6 \\ y_2 = 14 \\$
Substitute into the slope formula:
$m = \frac{14 - 7}{6 - 3} = \frac{7}{3}$

Therefore, the slope of the line is $m = \frac{7}{3} = 2\frac{1}{3}$.

The correct choice from the given options is: $m=2\frac{1}{3}$.

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

• Identify the coordinates of the points.

• Apply the slope formula.

• Calculate the slope value.

Let's work through the steps:

We are given two points on a line: $(5,7)$ and $(1,3)$.

Step 1: Assign the coordinates: $(x_1, y_1) = (5, 7)$ and $(x_2, y_2) = (1, 3)$.

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

Substitute the coordinates into the formula:
$m = \frac{3 - 7}{1 - 5} \\ = \frac{-4}{-4} \\ = 1$

Therefore, the slope of the line passing through the points $(5,7)$ and $(1,3)$ is $\bm{m = 1}$.

Thus, the correct answer is $\bm{m = 1}$, corresponding to choice 1.

The problem asks us to find the slope of the line passing through the points $(-5, 10)$ and $(0, 0)$. To solve this, we'll follow these steps:

• Step 1: Note the coordinates of the two points. Let $(x_1, y_1) = (-5, 10)$ and $(x_2, y_2) = (0, 0)$.
• Step 2: Apply the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Step 3: Substitute the values from the points into the formula and simplify.

Now, let's substitute and compute the slope:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 10}{0 - (-5)} = \frac{-10}{5}$.

Simplifying, we get $m = -2$.

Therefore, the slope of the line is $m = -2$.

To find the slope of the line passing through the points $(-2, 3)$ and $(0, 1)$, we use the formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$:

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

Substituting the given points $(x_1, y_1) = (-2, 3)$ and $(x_2, y_2) = (0, 1)$, we have:

$m = \frac{1 - 3}{0 - (-2)}$

This simplifies to:

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

So, the slope is:

$m = -1$

Thus, the slope of the line is $-1$, corresponding to choice 2.