To find the slope of the line that passes through the points [tex]\((3,4)\)[/tex] and [tex]\((6,16)\)[/tex], we will use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here's the step-by-step process:
1. Identify the coordinates of the points:
- The first point [tex]\((x_1, y_1)\)[/tex] is [tex]\((3, 4)\)[/tex].
- The second point [tex]\((x_2, y_2)\)[/tex] is [tex]\((6, 16)\)[/tex].
2. Substitute the coordinates into the slope formula:
[tex]\[ m = \frac{16 - 4}{6 - 3} \][/tex]
3. Calculate the numerator and the denominator:
- For the numerator: [tex]\( 16 - 4 = 12 \)[/tex]
- For the denominator: [tex]\( 6 - 3 = 3 \)[/tex]
4. Divide the numerator by the denominator to find the slope:
[tex]\[ m = \frac{12}{3} = 4.0 \][/tex]
So, the slope of the line that passes through the points [tex]\((3, 4)\)[/tex] and [tex]\((6, 16)\)[/tex] is [tex]\(4.0\)[/tex].
