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Find the slope of the line that passes through the points [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex].

Step 1: Identify [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex].

[tex]\[
(x_1, y_1) = (2, -5), \quad (x_2, y_2) = (7, 1)
\][/tex]

Step 2: Use the slope formula:

[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]

Substitute the values:

[tex]\[
m = \frac{1 - (-5)}{7 - 2} = \frac{1 + 5}{7 - 2} = \frac{6}{5}
\][/tex]

So, the slope of the line is [tex]\(\frac{6}{5}\)[/tex].

Sagot :

GinnyAnsweridn
Sure, let's find the slope of the line that passes through the points [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex].

Here's the detailed, step-by-step solution:

### Step 1: Identify the coordinates of the points

We are given two points:
- Point 1: [tex]\((x_1, y_1) = (2, -5)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (7, 1)\)[/tex]

### Step 2: Recall the formula for the slope of a line

The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

### Step 3: Substitute the coordinates into the formula

Substitute the coordinates [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex] into the formula:
[tex]\[ m = \frac{1 - (-5)}{7 - 2} \][/tex]

### Step 4: Simplify the numerator and the denominator

Simplify the expression in the numerator and the denominator:
[tex]\[ m = \frac{1 + 5}{7 - 2} \][/tex]
[tex]\[ m = \frac{6}{5} \][/tex]

### Step 5: Perform the division

Divide the numerator by the denominator to find the slope:
[tex]\[ m = 1.2 \][/tex]

So, the slope of the line that passes through the points [tex]\((2, -5)\)[/tex] and [tex]\((7, 1)\)[/tex] is [tex]\(1.2\)[/tex].
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