To find the slope of the line that passes through the points (7, 4) and (9, 7), we need to follow these steps:
1. Identify the coordinates of the two points. Let the first point be [tex]\((x_1, y_1)\)[/tex] and the second point be [tex]\((x_2, y_2)\)[/tex]:
- [tex]\((x_1, y_1) = (7, 4)\)[/tex]
- [tex]\((x_2, y_2) = (9, 7)\)[/tex]
2. Calculate the difference in the x-coordinates ([tex]\(\Delta x\)[/tex]) and the y-coordinates ([tex]\(\Delta y\)[/tex]):
- [tex]\(\Delta x = x_2 - x_1 = 9 - 7 = 2\)[/tex]
- [tex]\(\Delta y = y_2 - y_1 = 7 - 4 = 3\)[/tex]
3. Use the slope formula to find the slope ([tex]\(m\)[/tex]). The slope [tex]\(m\)[/tex] is given by:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
Substituting the values we calculated:
[tex]\[
m = \frac{3}{2}
\][/tex]
So, the slope of the line that passes through the points (7, 4) and (9, 7) is [tex]\(\frac{3}{2}\)[/tex]. This can also be written as 1.5 if a decimal form is preferred.
